As a quick test to check whether you have issues with insuficient power supply capacity, and if you have the chance, try making experiments with different telephony operators (e.g replacing current GSM module SIMcard by another) which do not share the same radio base station antennas. If incoming signal strenght is weak, it will force the RF stage of the module to drain more power.
Anyway, just out of curiosity, I would suggest you try monitor received data with a terminal capable of displaying non ASCII data just to check if there exists some pattern on the "garbage" characters, even thought from the images above it seems to happen quite randomly.