On 4 of my 7 captains, transwarping to the Alpha quadrant is a real ball ache and basically impossible. They all (except for the Jem'Hadar) have a TW listed as Bajor, but it doesn't work. That is, on my Vulcan sci, Human eng, and Joined Trill tac, selecting the Bajor TW point does nothing whatsoever. On my Fed-Rom however, picking Bajor sends her to Defera, and yes, the Defera TW option sends her to Defera as well. The Jem'Hadar has a DS9 jump which works just fine, and the last 2 captains aren't high enough to have access to Alpha yet, so can't test the TW for them.
What's even more strange: the auto-nav doesn't work at all for my Trill in the Alpha quadrant. I can pick a system and tell it to go there, but it will never turn and just goes in a straight line until it hits the edge of the map (and then keeps going even when the "can't go there" message pops up). Works fine in other quadrants, but in Alpha I have to do manual navigation only with her.
Happens persistently all the time, every time I've tried it.
Probably worth mentioning that my human eng was made on the day the game went Free-to-play, but the vulcan, fed-rom, and trill were all made much later, but still before the map was changed to what it is now. I haven't played in close to two years, but the Jem'Hadar and the little ones were all made in the past week. The Jem'Hadar (Vanguard) has a bunch of other bugs, but his TW works fine.