Epicbob, I can see you've got 5 pages of replies to this question. I've not read them; I'm simply going to answer your original question. These are my observations regarding 9 of the points from your post.
when we're taking a long time to figure out a solution to problems (for whatever reason), he tends to get mocking and sarcastic because HE (and/or his other experienced friends) would have long solved that situatition.
That doesn't sound fun to me. I mean, if it's playful because you guys really are acting listless and aimless, then sure, I can see some friendly ribbing to get you guys to engage. However, if he's just gloating or something, that doesn't impress me. I was running a game for some friends, and they were at a loss regarding the next step for a quest. Rather than mock them, I left them hanging for about 10 minutes, and when it was clear they were banging their heads against the wall, I said, "OK, everyone roll intelligence checks. I will see if any of your characters have more insight than you do." With a couple of decent rolls, I handed out a hint. It wasn't a flat out answer, but it indicated a line of thinking they could explore. They did, and eventually found a good course of action.
I believe a good GM will do things to keep the game moving. A GM is not running a fun game if he mocks players as they get stuck and the game crawls to a standstill.
in combat, he's nitpicky about pointless stuff. for example :
DM : Which Goblin do you attack?
Me : (with my bow) The closest one.
DM : That's not specific enough.
Me :

fine...Goblin number 1.
DM : Dude, i shouldn't have to tell you that you have to choose betwen the melee Goblins and the ranged Goblins. you have to make sure you know this and if you can't understand my subtle hints, it's your problem.
Me : (to myself) are you




ing serious???
To be fair, this sounds like shared stupidity, all around. On the one hand, it really is reasonable for a GM to expect players to know the game rules -- if they don't at first, OK, explain some as they come up. However, you have written that you are on your 3rd campaign with him. You should have shown some curiosity and initiative about the rules, so that you can take care of your own character and his actions.
For me personally, I will babysit new players for a while, which can be as short as 1 game or as long as 20, depending upon charisma (of the player). However, there is a point when I expect them to either crack open the book or bow out of the game from disinterest. "I want to keep playing but don't want to read anything" is not an approach I'll accept from players after a while. Players that are like that are not invited back.
On the other hand, he keeps inviting you back and then whines. That's annoying. If he wants you there, he needs to let you crash and burn instead of nagging you like a bitter spouse. If you say "closest one" to me in a game, then I'm going to take it literally -- the one with the fewest spaces between you two is the one you shoot. If that's sub-optimal, so what? You said what you wanted to shoot, so I let you. And I try not to be a jerk -- if other players chime in with hints, that's fine, you can restate your action (so long as it's still your turn and you have not yet learned the outcome of your decision). I certainly wouldn't go on a mini-rant about how I'm giving you hints and you're not picking up on them. I don't like playing "gotcha" games -- if something is so badly executed that I feel compelled to whine about it, I'd prefer of myself that I simply speak plainly and say, "Wow, you know that's a minus 8, right?" or whatever.
the rest of the fights, we almost always start toe-to-toe with the enemy, making my archery Rogue entirely POINTLESS.
If your game is D&D, you should know that 5' steps are free and don't provoke attacks, which means you can generally get back from melee and fire the bow without worry. Also, the tumble skill will get you into a free spot to shoot from, with no attacks as well. Harking back to the previous comment, if you didn't know that, it's not your DM's fault. He's doing it right by letting you play an archer sub-optimally. It's on you to get better at the rules that affect your capabilities.
If it's not D&D, then I have little to say. I don't know other rule sets. However, if those rule sets have a way for rogues to get through battle and shoot bows, you should know those rules by this point.
we get chased by Frost Giants...at level 1.
This is great! This is awesome! I think your GM is very cool for doing this. Why? Because I tire of safe, boring, balanced worlds. They lure the players into a lull of mindless fights where the assumption is that battles can always be won, so there is little need for critical thinking.
My campaigns do the same, though I make it clear to the players that they can avoid such risks by engaging their minds and being shrewd. For example, I ran a game where the players knew full well that the mountains were overrun with Frost Giants, but there was absolutely no need to head into the mountains. (The main quest path was somewhat balanced; it's just the outside regions that were more unpredictable.) Point is, if they wanted to pick a fight (or, commit suicide), they knew where to go. They chose to avoid the mountains.
I also left my random monster encounters unbalanced, as that's just the way the world is. If they got a 12-headed hydra at level 1, well, sucks to be them. The story of those heroes either ends rather un-heroically there, or else is about how they fled like hobbits from the nazgul, surviving to redeem themselves another day. I'm OK with this, and the players know I make my world like this. So when a monster appears, they
ask about it. They say, "Can I do a knowledge check? Did that first attack look like it was the best it could do?" and so on. They are sometimes genuinely
afraid of monsters, and that's fun.
Having said that, they also may get 5 wimpy kobolds ambushing them when they are level 12. Those are honestly some of the most hilarious, enjoyable encounters we experience. It's rare, but fun. Overpowering monsters all the time wears me out as a player. Everyone needs to experience variety.
during a mission for a dwarven mine, we get captured by Drows because we didn't specify we were Silent Moving.
That absolutely cannot be assumed in any game I run, so yeah, if you didn't specify, you didn't do it. I assume you move, breathe, and eat normally. Any time you are doing something different, you need to state the exception.
I had a player who was exploring a haunted house. He opened the door to a room and saw shelves on the opposite wall, lined with potions. Eagerly, he said he searched the shelves. Searching rules state that you have to search 5' squares one at a time as you move, so to execute the search, he was moving into the room. I said, "As you begin your search, you trigger a trap and...." he cut me off. He tells me he didn't go into the room. I counter that he had to, to execute the search. He says he really meant he was spotting from afar. Well, unfortunately Mr. Player, now that you know the outcome of moving into the room, and since you said one thing but meant another, you're stuck. Trap is triggered; be more careful next time.
the rest of the campaign was us getting carried to jail and publicly executed. he also spent a few hours on this sequence. which means we spent the REST of the session jerking off because there was NOTHING we could really do.
That sucks. That is utterly boring and railroady. I probably would have left halfway, or at least not returned for subsequent games.
we just left the region, got ambushed by way more bandit than we could handle (7 to 1 ratio), were left naked (except for a stick i found) and peniless. we walked to a nearby town where we went to a church an asked for charity. turns out the priest fetched a few guards to kick our ass (luckily we won). apparently the particular deity didn't like us or something. we dropped this campaign altogether.
I can't tell from the wording if the GM dropped it, or if the players said, "No, thanks." However, I'd be on the players' side here -- if they said no to being forcibly outmatched, robbed, and beaten by different groups (who seem to be unrelated but coincidentally were all ganging up on the characters), I'd have to agree with them. I can handle a bad thing happening. I can handle a short railroad off-stage (meaning, if the GM opens the game with a narrative about how the group was robbed and play picks up immediately afterward). However, having multiple bad things happen that undermine my character, and having them all happen as if unrelated enemies are magically coordinating their efforts, and having them all be forced failures even though I'm (ostensibly) playing, would drive me nuts. I'd probably stop the GM at some point in there and say, "It sounds like this is more of a story you're telling than a game I can affect, so I'm going to drop out now, OK?"
one was the sleeping quarters for the goblins with a high level DC that i BARELY managed to lockpick (you'd think one of the goblins we killed would have the keys to their own SLEEPING QUARTERS).
If this is D&D (and since you mentioned a natural roll of 20 later in your text, I'll assume so), then I have to say that lockpicking can be a "take 20" experience. It takes 20 times longer than a normal attempt, so instead of 1 round it's 20 (or 2 minutes), but nonetheless, it ensures that you get the best score possible. Again, this is something on you to know. The GM is not wrong if he did not tell you this, and it's not unusual to have doors that are off-limits initially, or at least which require a take 20.
Yes, it's weird that kobolds could get locked out of their own sleeping quarters. However, it's likely that they knew a secret knock or something to get it. Really, I wouldn't feel entitled here, as if the game or GM is rotten for not handing this to you. Bash the door down. Take it off the hinges. Stone shape the wall around it, or bash the wall itself. Get underneath the room and blow up the ceiling, giving you access. Charm a kobold and order him in. Turn invisible and slip in when someone else opens the door. I'm sure all these options were not available at the time, but at least some were, and if we want to sit here for another 5 minutes, I can come up with 20 more ways to bypass that obstacle.
That's part of role playing. Get inventive, think outside the box, try stuff and see what works.
so i ask...am i just weak or is the DM too unreasonable?
Both.