If your gutters have any cracks or holes, the seepage could cause structural damage to your house. You'll want to apply the relatively cheap and quick fix of repairing the gutters before any real damage is done.
First, wire-brush the damaged area to remove dirt and loosen rust. Clean the area well with a rag soaked in mineral spirits. If the hole is small, or if the metal isn't rusted all the way through, a screening patch isn't needed; just spread roof cement over the damaged area.
To repair an open hole in a gutter:
Step 1: Cut piece of scrap wire screening, 1/2 to 1 inch bigger all around than hole.
Step 2: Using trowel, spread roof cement around hole, and press wire screening patch down into hole. Spread thin layer of cement over screening. Let dry.
Step 3: If holes of screening are still open, spread another layer of cement over patch to close it completely.
If the gutter is extensively damaged or has a large hole in it, patch it with sheet metal instead of wire screening. If the gutters are copper, use copper for this repair. Use sheet aluminum for other types of gutters. Here's how:
Step 1: Cut piece of sheet metal big enough to cover inside of gutter completely and wrap around outside edges. Patch should extend at least 1 inch beyond damage each way along gutter.
Step 2: Bend patch to exact shape of inside of gutter.
Step 3: Use roof cement to coat entire area inside gutter where patch will go, then press patch down into cemented gutter to cover hole.
Step 4: Bend edges back over gutter lips with pliers, then coat entire patch inside gutter with roof cement. Make sure edges of patch are well covered.
Besides patching obvious damage, inspect gutters for sags, loose sections, and loose hangers. Gutters are held by sleeve-and-spike supports, fascia brackets nailed to the face of the wall, or strap hangers nailed to the roof.
Loose hangers can be adjusted or renailed; use 6d galvanized roofing nails to reset them. Cover the nail heads with roof cement to prevent leaks. If you can't get at a fascia bracket to renail it or if the gutter sags even though all its supports are solid, add supports. There should be a support about every 21/2 feet along the gutter. Make sure you cover all nail heads with roof cement.