Tunebooks are great - every session should have one. (Pip Radish)
Agreed to a certain extent, but stagnation can also set in (if it's twenty past nine it must be 3x Staten Island going into 3x Soldiers Joy) unless there's also the freedom and willingness to have new tunes introduced. Even if it's a beginners' or slow session I'd suggest that the occasional new tune is a bonus to keep stretching people and improving people's repertoire, but that can be 'managed' if necessary by updating the tunebook.

If it's a open session, I find the best are those where the majority of the tunes are familair to a greater or lesser extent, and some are new tunes. If it's a good tune and people like it, it will 'stick' and worm its way into the core repertoire.

Nothing worse than starting a tune, finding you are on your own because no one else in the room knows it and then nerves get the better of you and "finger fumble" sets in. (Tootler)
Again, agreed to a certain extent, but as you get more practised and confident in your playing you can Fight Finger Fumble. The way I get round the situation you describe is to play through the tune a couple of times then switch to one that I'm pretty certain people *will* know. That and being sufficiently cussed to think well *I* think it's a great tune, you might like it and want to pick it up, and if not there'll be another tune along in a minute of course :)