Forgot to add what the Packers generally look for at the position. There could always be exceptions (Cobb broke the WR must be at least 5'11" rule a few years ago), but these are kind of general rules.
Packers traits: Thompson generally brings in QBs that are at least 6'2" with solid accuracy and solid mobility who fit a precision passing scheme. He has gone outside these when taking late round fliers on Ingle Martin and B.J. Coleman, but they haven't worked out.
The QBs in this draft that fit these criteria:
Derek Carr, Teddy Bridgewater, Blake Bortles, Jimmy Garoppolo, A.J. McCarron (barely on mobility), Garrett Gilbert, Bryn Renner, Brendon Kay, and Brock Jensen.