I think that's a very good question, and I would argue that the few answers somehow reflect the lack of well established QC methodology in proteomics (although there might be few people working in that field on Biostar), especially compared to genetics and transcriptomics. A precise answer will also depend on the sample (simple or complex mixture) and it's processing (enrichment for instance).
Probably the very first thing to do is to look at the raw data, as it is produced from the mass spec, i.e the elution profile and the raw spectra. I am always amazed how our in-house mass spec specialist can comment on the raw data and quickly assess how good the results are, or at least if the data is good enough for the question considered. To do this, you really need to know what you are running in the first place and be aware of the capabilities of your machine. Mass spectrometry is still a hands-on experiment, in comparison with more mature technologies (and technically easier) like microarray. Of course, all this requires to be where the data is generated, which might not be the case if you work as a bioinformatician and take care of data repositories for example.
IMHO, there is need for more QC steps because (1) not every body has an expert to ask and (2) having automated pipelines, that statistically asses QC for single or multiple data sets, is crucial. I think that delta m/z differences, precursor charge assignments, PTMs, MZ distributions,... as you mention, are a good start. Still , it would be important to formalise the knowledge of the mass spec gurus and implement it in programs. And btw, PRIDE inspector is a good means to quickly assess public data for meta-analysis.
Finally, you might be aware of a recent special issue of Proteomics about QC. I have not had time to read it thoroughly, so I can really point to any specific method.
Hope this helps.