Check the eaves of the house before you move on to the actual slate shingles. Put the ladder against the wall of the house and work your way up to the point where you can physically inspect the eaves where the guttering is installed. Look for water damage that could be a sign of faulty flashing or worn-out caulking, and manually check the slate shingles along the edge for movement.
Visually inspect the shingles from your vantage point on top of the ladder. Do not attempt to step up onto the roof, as this will cause damage to the shingles and potentially cause the slate shingles to crack, which will introduce water damage. If you see pieces that look like they are out of place or somehow damaged, mark their location with a tape measure. Also look for buckled areas where the roof may be caving in from the weight.
Inspect the flashing along the edges of the chimney (if you have one). The adhesive keeping the flashing in place against the chimney should be snug and tight, and the caulking should not have cracks or voids in it. If possible, pry at the flashing with your finger gently to ensure it is still adhered sufficiently.
Enter the attic of your home. Use a flashlight if you don’t have lighting. Check for water damage on the underside of the roof. This will be visible as dark, stained spots on the wood that makes up the platform on top of which the slate tile shingles are installed. Also look for water-damaged roof joists that may be causing any external sagging. Check the interior of the chimney for any leaks and bad flashing or caulking on the interior.