I have the same model, picked up at a hamfest for $20. Starrett is a well known brand and made quality metrology tools, especially when that one was made. Aside from damage due to wear or misuse, there is little that can go wrong with one of these.
The jaws should be parallel, as determined by closing the cleaned jaws and holding to the light. You shouldn't see any light coming through the jaws. Another way to check that were were taught in metrology training was to gently grab a gage block in the jaws and hold it with the jaws horizontal. If the gage block rotates, the jaws aren't parallel and the tight spot is the point of rotation.
The vernier should be properly zeroed when the jaws are closed. As to proper calibration with a set of gage blocks, I wouldn't worry about that. I haven't seen a set of gage blocks that can calibrate the full range of a 24" caliper anyway. People seem to forget that this is a hobby machinist site.
To check calibration, I would use some 1-2-3 blocks, verified with a micrometer. A stack of two will give you calibration points at one inch intervals up to six inches. If you're good at those points, you should be good the rest of the way. Alternatively. you could mike a six inch parallel and measure that.
If you are in a production situation and require ISO9000 certification, you are most likely having a certified metrology lab do your calibration anyway. Otherwise who's going to argue with you if you say a chunk of steel is 22.364" long?