The Teriyaki Beef Bowl & the fried dumplings (Gyoza) are very good and very reasonably priced. The Panko Fish is also quite tasty, but I've had better fish at other nearby places (like Karim's) so I wouldn't bother to go to Blue Fin for fish. I've also had the Chicken Teriyaki Bowl before, but didn't find it too tasty. Coworkers have commented to me that the other chicken dishes are not to their liking, so perhaps this is a weak point for them.
Your best bet is to pick the food up to go as the inside is very small (and not aesthetically pleasing) and the place gets quite busy during lunch time. The food here is decent and the food reasonably cheap so we keep going back, but it's not really high on my list of preferred Asian places.
P.S. This place seems to attract a lot of Phoenix's redneck population (though I don't know why), so just be prepared if that sort of thing puts you off!