I have a few places on 1/2 copper water pipes in my basement that look rusted, right where a strap is. Should I be concerned enough about a leak to replace the line?
I'd replace the strap with a copper strap placed adjacent and clean up the copper pipe before deciding.
I expect it is superficial, copper tarnishes rather than rusting and pinhole leaks start from the inside.
I completely agree with aaron! Additionally & it may just be me, but it looks like it's nailed into ductwork. If so, then this should NOT be repeated. A much better option would be to screw-on a 1x2 (or whatever) deeply notched or slotted piece of wood to the end of that 2x4...a flat or straight piece of wood is fine but you'll want to put RedGrittyBrick's copper clamp on top of it to lock the pipe in & down.
Actually clean & sand or very cautiously & lightly grind that copper pipe to remove all foreign contaminants. Screw a plastic spacer (using the old duct nail holes) between the pipe & duct work or seal the duct holes & wrap the pipe liberally (to make a space) with electrical or duct tape around the cleaned pipe.
Repeat this &/or RedGrittyBrick's instruction at all other very big & yes leak waiting to happen problem areas.
Very often a situation like this is an early warning, that indicates you've got a serious galvanic action going on inside the pipe as well. If your system isn't grounded properly and the anode's spent, you could end up with thousands of pinholes all through the whole system, and thousands of dollars of repair expenses. Catch that NOW and you'll be fine.
So, make sure you have a thick copper jumper wire between the inlet and outlet pipes of your water heater (and across the inlet and outlet pipes of your water meter if you're on city water) and check the sacrificial anode on your water heater. If you don't understand what that means, google the hell out of it.
Make sure you replace all those steel clamps even if you do find that your anode needs replacement. There should be no steel in contact with your copper lines if you can possibly avoid it.