Looks like the console is showing it's age. Got to remember these things were built in the early to mid 1970's so many things are slowly decaying in them. My Atari Super Pong from 1976 does the exact thing sometimes with a nice long paddle that covers the screen, kind of cheap considering the ball can never get past it xP
If your playing on an LCD, problems are going to show up easier since Pong is a console that relies on some very low interlace TV rates so, you may or may not see the ball or other things in motion on a newer LCD, CRT's are still the best bet.
Ask for the main problem problems itself, three things most likely to fail in Pong consoles, Potentiometer, which are the knobs that control the paddles, the switches, which control game modes, and capacitors. Most likely the contacts on the potentiometers and switches are worn to hell so you could either try taking them apart and cleaning the contacts which is easier said than done. You can also try to find a replacement for them all but they very hard to replace since I have no idea where those specific pedometers and switches are sold, maybe someone else here does?
And the capacitors, well it's always nice to replace those since lets face it, you don't want them to dry up and cause electrical problems or burst for some reason, and there's very few on the board so, not much work to get those in place.
Hope some other tech people here can suggest some other useful info for you!