I've got a basement full of old half-inch copper pipe, and some
of it needs to be replaced. I want to do repairs in 3/4" pipe
but I'm wondering if that will cause problems with the water
changing pipe sizes on its way to an outlet. Can I do this?

It will cause a problem if there are long runs on the Hot side.
3/4" pipe has roughly 50% more area than 1/2", meaning that
50% more volume of water has to be drawn from a distant faucet
before Hot water arrives. *That may be trivial or it may be a
real pain in the neck.

OP-
Speedy Jim is on the right track about 3/4" vs 1/2" (both nominal
size copper tube) but unless my calcs are wrong...the 3/4" tube
will have closer to twice as much cold water volume to clear.
This will double your hot water wait time.

Why does the copper need replacing? acidic water? leaks?

There is white crud coming out of some of the copper joints. What is
that? I expected green corosion instead. Should I replace all those
joints?

But my primary leak right now is where a water pipe has been touching
the conduit for the main house power for fifty years or so, and the
contact has caused a pinhole leak, of 5 or 6 gallons a day. I'm
looking at inserting a "universal pipe repair clamp" between the pipe
and the conduit, before I think about replacing sections of pipe.

I dont see why varying pipe size would otherwise cause problems.
cheers Bob

Thanks both of you. I'll have to look at how long the hot water runs
are.