Like what kind of problems?
Well, the biggest one is that unlike a fuel injected application with a fully-closed fuel supply system, a carbureted application has an open fuel supply system. If you have a problem that causes the carburetor to flood (stuck float, stuck inlet needle, etc.), the engine will stall. A mechanical fuel pump will stop pumping, but an electric one will keep right on pumping as long as it has power
it'll pump the contents of your fuel tank into the carb, which will overflow and spill into the intake tract and onto the (hot?) engine and street below. The same will happen if you are in a serious crash. Sure, "turn off the ignition", but you have to think about situations in which you might not be able to do so. This can be addressed with thoughtful fuel pump control circuitry. For a clean installation without any nonstandard dashboard switches, you use a couple of relays. One, a timer relay, closes for 2 seconds or so when power is applied and then opens. This causes the electric pump to pressurise the supply line when the ignition key is first turned to "on". The main relay for the pump gets wired with its trigger circuit contingent on the oil pressure sender's state. If there's a ground at the sender, then the pump doesn't operate. That way when the engine stalls for whatever reason, the fuel pump will quit running after oil pressure drops off (usually within a few seconds of engine shutdown). If your engine requires extended cranking from cold for whatever reason, you can also put in a relay bypass circuit fed off the starter relay, so the fuel pump runs whenever the starter is cranking, regardless of oil pressure. The smart installer also puts in an inertial cutoff switch that kills power to the fuel pump if the car is hit hard.
Putting in an E-pump also means looking at the charging system, which is pretty marginal and beleagured on many of our cars. Line voltage already drops at idle -- lights dim, heater fan slows, radio gets quieter and staticky, wipers slow down, and ignition quality gets poorer until the engine is revved up. Adding another steady load on the electrical system will aggravate all those symptoms as well as stressing the fuel pump motor (motors don't like undervoltage; it makes them run hot). This is not incurable, either; there are
perfectly good upgrades to be made to the alternator and the charging system wiring. But like proper control circuitry, it adds to the cost and complexity of "just put in an electric pump".
Then there's noise. Some pumps are noisier than others, but it can be harder than it might seem to find a quiet one and mount it such that you don't get chuckle or whine annoyingly audible throughout the car whenever it's running.
I just haven't (yet?) encountered the cold-start problem that couldn't be fixed without resorting to an electric fuel pump. Carb condition, choke adjustment, etc., and cold and hot starting on a slant-6 car get
way less bîtchy with the simple
fuel line mod.
