The menu here is misleading, as it uses the word "vegetarian" but does not disclose that every dish has either fish/oyster sauce or shrimp paste. That said, with the exception of the curries, all the dishes can be made vegan.
Taste of Thailand is probably the best Thai restaurant downtown (and one of the only ones, for that matter), and probably one of the better ones in Minneapolis. It slightly edges out Amazing Thailand in Uptown, in my opinion.
We asked lots of questions and had a wonderfully friendly and helpful waitress who checked with the chef about ingredients. First, as stated earlier, none of the curries are vegan or vegetarian, and cannot be modified (the curry pastes all contain shrimp paste). Even the so-called "vegetarian red curry" is not, in fact, vegetarian.
Also, all of the stir-frys have oyster sauce, but at least these dishes can be modified to be completely vegan.
We had a Pad Bai Kra Prao (basil stir-fry) with mock chicken and no oyster sauce ($10.50). I found the dish to be nicely seasoned and spicy; it felt like there was some authenticity and heft to this dish, which can easily be made bland by a lesser restaurant. The mock chicken was cooked well, though it looked and tasted exactly like mock duck to me.
We also had a Pad Thai with tofu, and no egg or oyster sauce ($10.50). I liked the Pad Thai quite a bit, as it had an array of flavors and tastes, spanning the range from sweet to spicy to sour, which once again suggested authenticity. Pad Thai can easily be made poorly, but this place managed to get the tricky balance of flavors just perfect. The tofu could have been marinated or seasoned more, but that's a minor quibble.
In the end, this is a good Thai restaurant, but make sure to insist on no fish/oyster sauce in the non-curry dishes. Avoid the curries all together if you are vegan or vegetarian and don't wish to eat shrimp paste.