At some point, your seamless gutters are likely to need repair. In order to fix problems with your gutters, you can either patch, plug or replace.
For holes that are larger than a nail hole, patching is probably the best method. While some people like to use pop rivets to attach a patch, these do put additional holes into a gutter, so they may not be the best solution.
Instead, cut a piece of flashing with tin snips so that it is slightly larger than the hole in the gutter.
Use roofing cement or silicone caulk to spread over the hole. Feather the edges. Bend the patch to fit the gutter, then settle the patch into the caulk or cement.
For holes smaller than a nail hole, you may not need to create a metal patch. Instead, use a generous amount of roofing cement or silicone caulk on a dry day.
Spread it carefully over the hold in a thick layer and allow it to cure for the recommended amount of time.
If neither of these repairs will work, or if the seamless gutters are bent, have broken hangers, or the downspout is damaged, then replace the damaged piece with a new one.