What are the consequences in quest skipping?

Joining a friend who is ahead of you in quests allows you to "skip" quests.

What are the consequences to this? Do you lose out on experience and first-time drops? Or can you go back and do those later?

No there are no consequences at all. You can go back at any time and begin the last quest you were doing by yourself and it will start you from whichever part you were furthest during that quest. If you've never had a first time drop from an act boss you will get it whenever you defeat that boss for the first time (Rares seem to only drop once, and only in normal) Achievements earned in a friends game are obviously kept, as are lore book and conversations that are counted towards achievements.

I know because I've done it with some of my alt chars and helped my friends out with achievements.

Also @Ashel Crossing Difficulties isn't an issue because lower difficulty characters cannot go up to higher difficulties (There is also a level requirement for each difficulty so you shouldn't simply get your friends to rush you to Diablo anyway) So there is no way you can miss out on the Normal Boss drops so long as you actually go and defeat all of them for the first time on normal.

You can return to any quest you've previously completed from the menu, via the Change Quest button beneath the Start/Resume Game button. You miss the experience, items, and achievements you might have received from doing those quests, but since you can revisit at any time, there's no permanent loss from skipping ahead.

To elaborate on the above:

• Quest experience is never lost, as quests always seem to give the same amount of experience when completed, regardless of how many times you've completed them before.
• You do not receive your 'guaranteed' rare(s) for killing a boss the first time in modes past Normal - this appears to be a Normal only thing. I'm not sure what happens if you kill them on a higher difficulty then return to them later - once the servers come back up, I'll check that.