@wpeng - it is all cell line dependent, some cells will not survive after reaching confluence, others will happily grow in an over-confluent state (e.g. HeLa), while others will stop growing once confluent, but then be able to grow again when split.
The reliability for experiments is a difficult one, it all depends on what you are looking at, but for most purposes, actively growing cells that have been treated in the best manner possible (i.e. split when needed, fed when needed, incubated under good conditions etc.), will give you reliable and most importantly reproducible results. Cells that have reached confluence may not do this, due to variable growth rates and metabolic activities.
I don't know about mutations so much associated with confluence, but there are changes in cell behaviour with the age of the culture, which I think is associated with methylation patterns of the DNA and probably mutation too (it would pay to check me on that though!). For this reason you shouldn't keep cells up for more than 10-15 passages and try to make new stocks at as early passage as possible.