How much do you really scrutinize all these +1's and bonuses and this statistical makeup? Personally me? I STILL don't notice the 3.x brokenness, and probably wouldn't know about any of that if I didn't go on message boards. What about you? Not saying things are balanced or not, I'm just saying it escapes me or maybe our group doesn't really care about that stuff and it's usually completely unnoticeable. I'm sure its a big problem with some people though, just curious.
If you didn't notice 3.XE's broken-ness, then yeah, you're not going to notice this sort of stuff.
I think it's a lot to do with individual mind-sets, and where your background is, and also whether enjoy genuinely analyzing things, or prefer to either ignore the details, or generalize about them.
If you're from any kind of gaming background where rules-mastery actually matters, and where rules change with some frequency, or are very very complex, then you probably have had to develop some degree of ability to analyze rules, to think of the consequences of rules, and to look at the maths behind the game.
That would include most TT wargames, but not really stuff like chess, where the actual rules are relatively simple.
I think with RPGs, another factor is how much you've been exposed to the consequences of badly-made rules - particularly where those consequences aren't just a "common sense" issue, but are a math issue, or something that is so fantastical that "common sense" approaches don't easily apply. If you've never had a game get messed up because a designer clearly didn't understand the consequences of a rules-design he made, you're much less likely to be keen on analyzing them.
Personally I'm pretty good at picking up "Potential Offenders", but I'll always have some "false positives" and miss some offenders too. As Mistwell has noted in other threads, a lot of stuff simply won't show up as fine or broken until the game is actually played.
[MENTION=371]Hand of Evil[/MENTION] - That's the problem we're discussing, you seem not to understand that. First off, is it the DM's job to think about balance when determining what PCs can pick race/class-wise? Not everyone would agree - some would suggest that if it's in, say "The Basic Set" or "The Official Book", it should already be balanced, and the DM shouldn't have to take precautions.
This was discussed at some length earlier in 5E's history, when some people felt that potentially-dangerous classes and races should be clearly labelled as such.
But that leads to another problem - many RPG authors are terrible at balance and do not know it. So they add something to a game, and don't understand how broken it is. If these professionals can't do it, why would we expect normal DMs to?
Some of us can, of course, but a lot of DMs just don't recognise balance problems, and few RPGs, certainly not earlier editions of D&D, train you to recognise them, because they usually operate on the basis that the RAW are pretty solid (which they often are not). I mean, here I am, highly experience with dozens or hundreds of rules-sets, understanding design principles, maths, and so on, extremely good at reasoning out the consequences of rules (by typical standards), and enjoying rules-analysis, and even I'm missing a lot of stuff, so to expect the average DM to be able to reliably pick out balance-issues before the game even starts? I don't think that's reasonable.
I won't even get into how DMs who feel the need to "balance" stuff aggressively but don't understand the rules very well often end up making things even less balanced.
EDIT - 5E proposes a VERY interesting solution to this, in the whole "Living Rules" concept, where they will apparently be monitoring the game regularly via surveys and the like to attempt to determine if stuff is seen as out-of-whack, but where they will, unlike 4E, be taking player sentiment into account, rather than just rules-designer analysis of whether something is functioning correctly (this is also unlike most on-going computer games, where typically player sentiment is largely discounted in favour of developers deciding "where they want the game to go" and so on).