Great customisation and good track design doesn't save the PSP version from mediocrity.
+: Online sharing options allow you to upload and download tracks, karts and characters (aka, Mods, which is what a character is called in this game).
+: Good presentation.
+: Story mode and its cutscenes and characters are enjoyable.
+: Decent gameplay.
+: Online multiplayer is possible.
+: Default tracks are well made.
+: Some nice music.
-: Gameplay has been downgraded and slightly messed with.
-: Weapons act and look more generic, most weapons act differently. No weapon level system.
-: Drifting feels clumsy-horrible and takes too long for its own good to adapt to. (I think that's the cameras fault though.)
-: Online multiplayer is very buggy. (One race crashed my PSP before it even started and another crashed it once the race was over. Also I can never seem to get the lobby working 100% right.)
-: Severe lack of polish in racing gameplay, both visually (animation quality mostly) and in controls.
-: Annoying gameplay and track creation glitches.
-: Sound design could be a whole lot better.
If you've never played the PS3 version, or hell even Mario Kart DS/Wii, there is small hope that you might actually somehow end up finding this an enjoyable racer. However if you have played either of the 3 (or even something like Crash Team Racing), you'll probably end up disappointed.
While there's no denying everything else about it is impressive and fun to mess around with, the gameplay for this version has ended up feeling like it's not trying very hard to retain the elements that makes the PS3 version so great but instead settles with trying to be yet another kart racer. You can actually easily consider this a completely different kart racer to the PS3 version, unlike how LittleBigPlanet PSP is very much the same as it's PS3 original.
(And just to not make this whole review just comparing, I actually played the PSP version before the PS3 version a long while ago last year, I still wasn't that impressed and had the same thoughts about the gameplay and glitches for the most part.)
Avoid it unless you're still interested and find it cheap, or you're really THAT obsessed with Modnation and kart racers and ect.
Else just get or stick with the PS3 version, or if you're looking for a portable kart racer for PSP, take a look at WipEout Pulse or Pure.
...Ok it's not really a proper kart racer, but it's the best PSP racer involving pick-up item weapons I can think of.