I don't use it often but a couple of nights (say 23:00 UTC) ago I was trying to find something and every video I tried gave some "There was an error..." message a few seconds into the clip.
The more common problem (it's been happening on and off for a year or more) we get is that videos get so far and just stop. It happens on different PCs and browsers and I think has happened on the tablet. My guess has been that it's probably something to do with our ISP but I've not been bothered enough to look further into it.
I haven't been seeing many error messages, but I've been having the issue where videos play so far and then just stop too. It seems to 'auto reload' and pick up where it left off. Not sure how the player is handling it but I imagine youtube has a vast farm of servers to dish out the streaming content, maybe if one dies or is rebooting or has capacity issues it does that and then has to switch to a different one.