Starting a few months ago, every now and then the check
engine light would remain on after I started my 2000
Explorer when it was cold.   At that time it would happen
perhaps once a week, and the light would remain on for
perhaps a minute.  Car ran, and continues to run fine, at
about 140,000 miles.  The check engine light now comes on
almost every time I start the engine cold, and usually the
oil pressure needle remains flat for a minute or so and then
jumps to its regular position.  Oil level is fine, and I've
driven a couple of thousand miles without a problem since
the oil pressure needle became slow to get on station.

This never happens the second or later time the same day,
only when the car has sat unused overnight.

My mechanic says it is nothing to worry about.  I passed the
California smog check test a few weeks back.

Any thoughts/comments from the experts here?

Thanks.