Okay, lets address this point by point. Warning, might get messy, as I am on my phone and typing on it sucks.
1. Run by me again how Tai has Narcisstic PD?
2. work behavior: to be fair, it doesnt sound like there is much to do at the library. On the other hand, Marten is shown to impart a lot of knowledge on the interns (I am not going to browse the archives right now, but the strip included something about dental dams, condoms, the black bin and dodgeball). It can safely be assumed that Marten did not get his knowledge out of thin air. It would appear instead that he was taught by a knowledgable superior.
Also, she is hardly out of line in a place where they have extra bins for dental dams and condoms and where a teacher shags the headmistress (or something to that extent).
3. group sex: someone, you say that like its an inherently bad thing. Wtf?
4. going after Dora: as far as I remember, Tai asked Marten for permission. If not before, then at least after the first hint or something like that. That is more than Dora did. Dora was like "Faye doesn't want Marten? Okay lets kiss him. Oh, wait, that happened." Then without missing a beat she was asking Marten "okay, how do we make Faye not kill us both?" Now, my memory may be misleading me on those points; feel free to correct me. But she hardly qualifies as a "vulture" in my books.
5. cheesy line: how is the choice of words important? Instead shouldn't she rather be admired for having the guts to go after her subject of desire, after the last time she opened up to Bailey, Britney orwhatshername she basically had her heart broken?
someone: it sounds like there is at least a little bit of projection involved. Now, as was broadly discussed here during the Marten-Dora-breakup arc, the comic is our collective Rorschach chart, so of course you are welcome to do so. But by talking about characters like this, yo are hurting feelings of people in real life who like that character. Please try and be more attentive to that, okay?