Single-Word Requests – Word or Phrase for the Activity of Hiding Mistakes

The noun "pastime" actually describes activity that is pleasurable.

pastime

an activity that someone does regularly for enjoyment rather than work; a hobby: his favorite pastimes were shooting and golf.

To describe an activity that is used only as a diversion while letting time pass, you can say you are doing something to kill time.

kill time

to do something which is not very useful or interesting while you are waiting for time to pass

Or you can just say you are idling, or, lollygagging.

lollygag

spend time aimlessly: he sends her to Arizona every January to lollygag in the sun.

Personally I don't think there is any word that describes an activity which is not pleasurable and used only as a diversion while letting time pass as when you want to kill time, you don't do things that are particularly not pleasurable, but things that have no purpose.

I end up having to do this quite often and when I do I slurp. It may not be attractive or polite, but slurping is what the circumstance calls for especially for hot drinks, even if straws are available. Slurping not only allows spill-free drinking, it also cools a too-hot drink (unlike a straw).

Slurp - To make a sucking noise in drinking or eating (OED).