Don't Count on Caulk!
Rarely will caulk or roof cement cure a roof leak?at least for very long. You should always attempt a 'mechanical' fix whenever possible. That means replacing or repairing existing flashing instead of using any type of sealant. Only use caulk for very small holes and when flashing isn't an option.
Fix Small Holes
Tiny holes in shingles are sneaky because they can cause rot and other damage for years before you notice the obvious signs of a leak. You might find holes left over from satellite dish or antenna mounting brackets or just about anything. And exposed, misplaced roofing nails should be pulled and the holes patched. Small holes are simple to fix, but the fix isn't to inject caulk in the hole. You'll fix this one with flashing.
Leaks Around Brick Chimneys
All kinds of bad things can happen around brick chimneys. In fact, there are far too many to cover in this story. Flashing around chimneys can rust through if it's galvanized steel, especially at the 90-degree bend at the bottom. A quick but fairly long-term fix is to simply slip new flashing under the old rusted stuff. That way any water that seeps through will be diverted. The best fix, though, is to cut a saw kerf into the mortar and install new flashing. Get complete instructions on how to install chimney flashing.