A spellthief is no better or worse in Pathfinder than in D&D 3.5
The spellthief (Complete Adventurer 13–20) for Dungeons & Dragons 3.5 is considered by most fans a tier 4 class: versatile enough to solve some problems, yet often so focused as to be at a complete loss if her one cool shtick—dealing sneak attack damage to swipe magic—doesn't work.
Were the class transitioned to Pathfinder, this doesn't change. A well-played trickster spellthief will likely still find herself kowtowing to the party's alchemist or inquisitor—which are more standalone tier 3 classes—, but in the right circumstances a spellthief's abilities in such a party will still turn the tide of the occasional conflict.
Let me address your concerns:
"A spellthief can double the spells a party's caster can cast in a round!" Only by using the supernatural ability steal spells on another party member can the spellthief do this. The spellthief can, "[i]f the target is willing,… steal a spell with a touch as a standard action" (CAd 16)—so using the steal spells ability even on an ally consumes the spellthief's standard action—, and "[a]fter stealing a spell, a spellthief can cast the spell himself on a subsequent turn" (ibid. and emphasis mine). Thus the spellthief's steal spells ability can be used as precombat buff that leaves another party member voluntarily weakened, but using the steal spells ability against an ally doesn't break the action economy during an encounter.
"The spellthief casts sorcerer/wizard spells, and that allows a spellthief to cast, for example, the sense vitals spell and the invisibility spell!" The typical spellthief's caster level is half the spellthief's level, and the typical spellthief doesn't cast 2nd-level spells until at least spellthief level 8. Even in a campaign with an very low optimization ceiling, this isn't a big deal. Further, to be clear, the typical spellthief only casts spells from the schools abjuration, divination, enchantment, illusion, and transmutation. This eliminates all the conjuration spells (including the spell teleport), necromancy spells (including the spell animate dead), and all the evocation spells (including the spells contingency and force wall). In short, don't worry about stepping on the party wizard's toes: he still has plenty to do!
"The steal spell-like ability ability will trivialize some encounters!" Good heavens, let's hope so! Had the rogue made a full attack against the same foe that the spellthief did, the foe would be dead! And that usually ends the encounter, too! So, instead of killing the foe, the typical spellthief merely debuffs the foe. While that's a cool effect, the foe continues existing, and probably has more than just that tool with which to kill the spellthief. Also, keep in mind that unless the spellthief identifies beforehand what spell-like abilities a creature possesses and declares that those will be stolen, what spell-like ability the spellthief steals is random (although it's always at least one if one's available of a spell level the spellthief can steal) and the spellthief's limited to stealing spell-like abilities that have spell levels no greater than 1/3 her spellthief level (so never 7th-, 8th-, and 9th-level spell-like abilities).
The only thing that a spellthief really has going for her in Pathfinder that she doesn't in Dungeons & Dragons 3.5 is a host of new and different options for the feat Improved Familiar. An improved familiar is often the source of a typical spellthief's noncombat versatility. A lyrakien azata, for example, has some absolutely nuts spell-like abilities to steal, and the feat Familiar Bond (and—sigh—the feat Iron Will) then the feat Improved Familiar can—with a barely generous reading of the feat Familiar bond—get the spellthief such a beast at spellthief level 8.
(That lyrakien azata, for example, when the spellthief is level 8, allows the spellthief free use of spell-like abilities that can still matter, like cure light wounds, lesser confusion, silent image, and ventriloquism. At spellthief level 12, add the spell-like ability freedom of movement. And at spellthief level 18, add the spell-like ability commune—which would be gamebreaking were the game not just about to end.)
I can say with some confidence that only the most fragile of Pathfinder campaigns will collapse if only the spellthief class as presented in Complete Adventurer is imported into it. I imagine such a campaign to be extraordinarily caster-rich and those casters, to defend themselves and their holdings, conjuring vast armies of creatures that possess spell-like abilities. A spellthief in such a campaign could use his abilities all the time… and see himself be a constant target of casters' hatred. I can't see this as being unbalanced, either, as such a campaign will be horrendously deadly anyway. (Also, as an aside, in such a campaign, the player would likely still be better off playing a full caster as such a campaign removes much of the social baggage that typical campaigns—with rarer magic—usually carry.)
The variant class trickster and the feat Master Spellthief
An argument can be made for the spellthief variant trickster (Dragon #353 85)—that sees a spellthief's spellthief level equal its caster level, the spellthief use the bard's spells per day, and adds the bard's spell list to the normal spellthief's spell list—being tier 3. In a campaign with a very low optimization ceiling, this could be unbalanced… but such a spellthief likely won't be any more unbalanced than a typical Pathfinder bard who will have vastly more system support.
The feat Master Spellthief (Complete Scoundrel 79) is more problematic, but the tech that's used to break the game with the feat is, so far as I'm aware, absent from Pathfinder to begin with. So unless even more of Dungeons & Dragons 3.5 is being allowed into that Pathfinder campaign, even the feat Master Spellthief won't cause the campaign to topple.