GPS QA during manufacturing

There is no free lunch here. You need a solid test plan. This is an area well worth investing in, because once you develop a reputation for shipping shoddy products, it's pretty much impossible to shake it.

To a large extent, you need to be able to trust your component suppliers, and focus on testing only for the types of errors that occur during the assembly process, including wrong/missing components, poor soldering, etc. Visual inspection is one method that can be applied here, but there are also automated electrical tests that can be used to find a large majority of the potential problems. But if you are using unreliable suppliers, then you must invest more resources in incoming inspection and test.

But there's no substitute for a full-up functional test at the end, at least on the initial batch. If you find that your failure rate is low enough, you might consider only spot-checking subsequent batches, or dropping the functional test altogether, but you need to balance that against the risk and cost of the resulting customer returns and dissatisfaction.

That is, no contact. I've currently come across 2 cold soldering and 3 no contact issues.

Looks to me you have got a hole in your final testing. (I assume you have some sort of test-jig)
I can imagine that waiting for a GPS lock requires too much test time but, especially with the detected errors you should add a resistance/contact/SWR test on the antenna.

There are few methods to accelerate GPS module assembly testing:

• Use AGPS to acquire a faster fix. TTFF should take few seconds, assuming you can load the AGPS data to the unit.
• Read the GPS raw data, specifically, C/n.
• Use a GPS repeater, or better yet, a GPS constellation simulator to get a known signal.