Plumbing issues seem to be one issue that a fair number of landlords get contacted about and that, if a landlord wishes, they can address themselves. These are fairly simple repairs; a leak under the sink, a clogged sink, a running toilet. Tools such as a pipe wrench (to tighten leaks), flappers (to replace a running toilet), toilet "guts" (these can also wear out) are handy to keep around. A simple toilet plunger is what we use first to try to clear a clogged sink (although sometimes one has to remove the p-trap under the sink to find the clog). If that doesn't work I really like the product called "Thrift"; it's pure lye and activated by pouring it into the sink and following it up with boiling water (stand back when you do this). Some use "snakes" to clear a clog.
Many landlords don't care to address electrical issues but often these might involve replacing an outlet or a light switch that have bit the dust. Not a difficult job but throw the breaker (and check you've thrown the correct one) before attempting.
And while this sounds strange, keep lightbulbs handy. Nothing like going into, say a bathroom to address a repair and that light you put in that once held 3 bulbs now has 2 burned out and the tenant hasn't replaced these. We now make sure to use LED bulbs (Daylight) in all the fixtures prior to a tenant moving in but still these don't last forever.