As noted in the release notes for r1060, there is indeed a problem with dual-headed setups. If the editor window is on the secondary monitor, the menu is displayed on the primary monitor (in the correct screen location, just on the wrong screen). On the plus side, if the editor is on the main monitor the menu works properly... This is on a MacBook running 10.4.6.
Console.log output:
2006-06-05 11:39:31.625 TextMate[3581] Quartz {1733, 123} (frame {{1280, 0}, {1280, 768}}), QD origin {1280, 768}, QD top/left 645, 453
scott.