I have noticed (with slight alarm) input audio coming out of the speaker while recording. I either use a headphone adapter or just keep the headphone gain pot turned all the way down to silence it. Still suprised there isn't a switch (menu or physical) to disable the speaker though, since there is on other Tascams like the DR-2d, and it would be more likely to cause a feedback condition for applications this machine is designed for, so it seems like something of an oversight to me.
The headphone output isn't great but is usable. Although it uses a smoothly variable pot, the gain changes are not smooth but exhibit rather coarse digital steps which are noisy. It has enough output to drive Senn HD650s decently enough though and as long as I don't need to adjust playback level with the headphone knob while listening it's okay. Actually, cranking it up the headphone knob and adjusting level using the monitor mixer stereo master instead is smoother and more acceptable for me. However doing that might get too hissy with lower impedance phones which will be louder at any given knob position than those 600ohm Senns.