3.0 is perfectly playable, and lots of fun. I played in many 3.0 campaigns.
Now, 3.5 was clearly made to fix some issues with 3.0 that came up over lots of play. Lots of them were fairly minor and would only come up with lots of play, especially high-level play. If you're sticking to a normal 25-point buy game, especially staying at relatively lower levels (under 10th level or so) most of the time, and not trying to min-max a lot it will work great (I get the suspicion that these were the circumstances it was mainly playtested under).
A 1st through ~10th level campaign, done with core-rules classes and races and a 25 point buy, with PC's not min-maxing and generally staying single-classed (or at most two-classed for non-spellcasting characters) will work pretty flawlessly and you may wonder even why they made a 3.5.
Some spells are ridiculously powerful, especially higher-level ones but a few at lower levels too. Haste is the most famous overpowered spell, but Harm has an infinite damage capacity, and Disintegrate is a save-or-die spell that can kill virtually anything (except Gods, since specific immunity to Disintegrate is a pretty rare immunity) since it's not a Death effect (I saw the climactic battle of many-session running of the Return to the Temple of Elemental Evil module end in one round when a PC hit module-boss-villain Imix with Disintegrate and he failed his save, since the writeup of him didn't include immunity to that spell).
Many base classes are more "front loaded" than 3.5, meaning that you can take one or two levels in a class then multiclass out, and with lots of multiclassing you can create some truly bizarrely classed monstrosities of PCs with lots of power (especially with a very literal reading of some rules, that was popular in some gaming circles when 3.0 game out). Example, the Cleric Domain rules just said "per level" instead of "per cleric level", so for things like the Strength domain's strength bonus or the Death domain's Death Touch a literal reading could mean you could have one level in Cleric, take the Death and Strength domains then go up in other classes, and have a once per day uber-strength bonus and a big death touch. Note how in 3.0 the Wizard Toad familiar gives a Constitution bonus instead of Toughness as a feat, that's a pretty beefy bonus for a familiar.
Multiclassing can break the game, in either direction. Prestige classes like Arcane Trickster and Mystic Theurge (and Cerebremancer) are the fixes put into D&D to let spellcasters multiclass, and in 3.0 they don't exist so you can seriously cripple a PC by making him part-spellcaster part-melee, and as I said above, with creative multiclassing you can make some unholy chimera character that can make the rules scream.
