Yes, you can use a multimeter to check your soldering. Just use the resistance/connectivity setting. If your multimeter has multiple resistance/connectivity settings, use the highest Ω (ohm) setting it has. When you check each connection, a reading of zero is good and a reading of infinity is not.
Also, make sure you've used the appropriate length and thickness for each of the wires. All connections except for power and ground should be #30 AWG (preferred) or #32 AWG Kynar or wire wrap wire. The power and ground connections should be #20 AWG (preferred) or #22 AWG of the same type, and should also be as short as practically possible.
In that case, it's probably just because you used crappy media. Use a different brand (better quality) CD-R and see how that works.