Are these black marks near an electrical box signs of an electrical problem that I should be concerned about?
That does look as if it could be soot. The wires themselves don't look damaged (melted, charred).

So there may have been some kind of appliance or device plugged into an outlet there, which failed and caught on fire, which presumably also damaged the receptacle. Or the receptacle itself may have failed and started smoking. In either case, the receptacle was never replaced, possibly just because it wasn't convenient or the previous owner never got around to it, or didn't know how.

There wasn't necessarily an overcurrent condition. But if there was, it could have been due to all kinds of transient conditions.

However, there's also a chance that the overcurrent was due to something like a floating neutral in your panel, which can be really dangerous. As in appliances spontaneously catching on fire or blowing up, and so on.

Do you have any electrical problems anywhere else in the house?

The wires in this box are connected straight through, which indicates that you probably have healthy receptacles further "downstream," in which case there's no reason why this box should be a problem with a new receptacle in it.

For peace of mind, you may want to hire an electrician to check things out all the way back to your service panel, to make sure that all of the connections are tight and you don't have any intermittent failures (like a cracked wire that carries enough current 90% of the time, but then overheats and moves causing voltage fluctuations).

If you disconnect the wirenuts, only one of the black wires should be live, and it should only show current when connected to one of the white (grounded/neutral) wires, and it should also show current when connected to one of the ground wires. Those would be the three wires that lead back "upstream" to your service panel. The other wires carry current on to additional outlets. In both cases (grounded and grounding, or neutral and ground) the current should be a steady 120 volts give or take a few volts, with or without a load on the circuit.