Behold ignorance:
I'm not that knowledgeable at all of Katy Perry, but when I tried to Ni an answer (intuit in a manner that brings all my subconscious memories and impressions to a semi-conscious level in order to guide me to a conscious decision?), I thought ESFJ. Sounds totally ridiculous, right? She'd be a very atypical and also unusual and uncommon ESFJ, but she screams Fe to me because she is so manipulative (her whole persona seems made up, all an act - i.e. catered to what people want, a.k.a. Fe (used to deceive for self-benefit)) and I decided S over N because she seems too in-the-moment reactive to be an N (Ne is in-the-moment reactive, but Ne and Se or S reactiveness is just different in ways I don't care to think of how to explain right now.
Then I watched the MTV interview (half so far). She definitely says a lot of random reacted things, but the things she says feel more mentally thought out than just plain reactiveness like an ESFP - so, I see Ne. But all of this randomness from her feels forced, so there's still a sense of falseness. As someone or some other people said before, I sense absolutely zero Fi from her. Her entire persona still seems all like a manipulation, a.k.a. Fe. So at this point, because Ne being her dominant function is unquestionable to me, I say ENTP. Her perceived in-the-moment reactiveness can be explained away with her being an N not an S as was my impression, if the face she presents is intended to be forced, meaning she is just "hyper-aware," i.e. aware she is forcing a persona, thus she is conscious of every behavior she acts.
I'm not saying just because I see Ne-dom-but-definitely-not-Fi I think ENTP, though. Ti in her doesn't stand out, but if you try to interpret her actions as having it, you can see her comments that she reacts with seem to involve logical analysis (T) of whatever situation or thing she is commenting on, and a deep, detailed/honed-in-like directive (introverted process, as in T
i, etc). Now on to Fe. As said before, she's always oozed of Fe to me. Remember it is often a person has an extra-developed third function. More often, the third function appears to be not just stronger than the second function but also seems to overshadow the second, which in her case it does if you consider her as ENTP (Ti's there, as demonstrated - she has Ti - but it seems so weak, minor, blah blah, where Fe is undeniable/obvious). Now, take her gender into account. Isn't there a bias for females to be F and males to be T? I don't really mean xxFx or xxTx, but in behavior (emotional/non-emotional and logical). With this in mind, it makes sense for her F function to be extra-developed at the cost of her T - social conditioning causing her to become more F than T. Additionally, I don't know user
Ethan all that well, but he's a male INFJ and his Ti always seemed extra-developed/strong to me (Male, T function development at cost of his F function, a.k.a. his third function, Ti, being stronger than his second, Fe - just as Katy Perry's third function which is her gender's function is stronger than her second function which is her opposite gender's. I also know a male ISFJ who seems to use Ti much more than Fe - again, third function typical own-gender used at the expense of second function belonging to opposite gender.).
But I'm not saying the actual Katy Perry is an ENTP. Or that it is just a stage persona (intentional,
deliberate manipulation). Either she is extremely, extremely skilled at putting on a false face (because even when people put on false faces, a lot of times you can tell what their real personality is/some realness leaks out subtlety), or her own identity to herself might be a little absent? Big claim, I know. Oh well. I theorize this last bit because I went and watched I watched another video of hers, this one short (
http://www.youtube.com/watch?v=PZeYkeD8WA0), and she maintained the same persona - randomly commentative/tangential/reactive a.k.a. Ne, and Fe/fakeness/manipulation still present. I'm not sure why this leads me to believe she might not have a solid attached identity, but whatever.

What I'm saying is unless she's a super actor, I think this is the closest to her "real" personality anything can be (ENTP).