Lots and lots of things to reply to here; please pardon the verbosity...
1. Define the "sweet spot". In our old 1e games, it was from about levels 3-7. With various tweaks and revisions to the 1e system, I think we've expanded it to about levels 3-9, but I'd still like to see it go a bit higher, say to 12-ish. In 3e, much has been done to smooth things out, including the sweet spot...now, I think one could argue there's about the same amount of "sweetness" from about 1-15, which is good, but that "sweetness" isn't as sweet as the old 1e 3-7 range. Make sense? OK, so how to either expand it (in older editions) or sweeten it (in newer)?
2.
Commune is a game-breaker from the DM's perspective, assuming deities to actually be the almost-all-knowing beings they're intended to be. It is very hard to design an adventure with any sense of mystery when the mystery can be shattered (or the puzzle can be solved) with judicious casting of one spell. I despise nerfing spells, and nerfing the deities themselves is just not an option. So, all that's left is to raise its level; in 1e I'd make it 7th (as high as Cleric spells can go) and in 3e it goes to 8th or 9th.
3. Travel spells (
Teleport, Planeshift, etc.) are a problem only if overused.
Planeshift is easy to fix: simply rule that it puts you back on any plane at the same place you last left it...this still allows parties to plane-hop but removes it as a travel spell.
Teleport is not a problem in 1e - the small risk of instant death tends to make people use it in emergencies only, and there's limits to what can be carried. Put the risk back in, and problem mostly solved.
4.
Raise Dead being available is not a problem *if* there's some chance that it will not work and-or *if* there's some overarching limit on how many times a character can come back. 1e handled the risk very well (Con-based survival % roll) and the limit not so well (can come back once per each point of starting Con., too high, in most cases). 3e just has you lose a level, with no risk of it failing and no limit (not to mention that in 3.0 the spell is ridiculously cheap; 3.5 at least fixed this); this makes it too easy. There has to be some mechanism available to revive dead characters, unless you as DM never plan on killing any; the Raise-with-risk works fine for me, even when the party can cast it in the field.
5. Level advancement rates. Obviously, slowing them down prolongs the sweet spot in any edition...so, particularly if you're playing 3e, slow them down; either by changing the actual bump points or by giving out less ExP per encounter. For those who've posted that their players "expect" the frequent gratification that advancement brings, I'll just be a curmudgeon and say that you as DM need to challenge those expectations - harshly, if necessary - right at the start of the campaign...and if the players balk, too bad for them.
6. Save-or-die is not a problem, and to some extent happens at all levels; it's only at the higher levels it becomes named as such. At 1st level, it's save (find the pit trap) or die (fall in and hit the spikes). At 5th level, if a bigass Giant swings at you, it's save (he misses) or die (he hits). At 9th, you're targeted with
Slay Living; save or die. It's all the same, really. More important is there need to be
other ways to die than all-or-nothing spells at high levels to keep the sense of threat in play; the simplest thing here is limit AC somehow (no idea how).
7. One thing that hasn't come up yet but is also relevant is treasure. Part of what makes the sweet spot sweet is that you've got *some* stuff as a PC, but you're hungry for more. At higher levels, often the PC's have most or all of what they need, so the hunger is gone. One obvious suggestion is don't give out as much, but this is
no fun. Instead, I suggest to give it out, but have it break/wear out/melt/etc. more often - easy come, easy go, and fun if the items sometimes release wild magic surges when they go.

Oh, and do away with magic shops if you have 'em; the only magic for sale would normally be stuff other parties don't want, and if other parties don't want it, chances are your party doesn't either. "What's for sale in Neverwinter?" "Well, you find the same +3 Footman's Pike that was for sale last time you were here; oh, and someone must have killed a Giant, because there's a suit of real nice +4 Hide Armour that just came on the market. If you're at least 13' tall, it'll fit you..." If they know the usual way they're going to find what they want is to adventure for it, adventuring maintains a bit more allure. (I'll admit I'm guilty of blowing this one...badly...)
All that said, the sweet spot is going to vary group by group to some extent. Some groups like nothing more than the sheer terror of trying to run 1st-level characters through a dangerous adventure, and by the time they're 5th it's not sweet anymore. Other groups think anything less than 10th is just preamble, before the real fun starts. As long as there's at least a vague agreement within the group, all's good. But I'm interested to note that others here have also pointed to the 3-9-ish range as being "sweet"; I agree.
Lanefan