I have an electronics manufactuing business (30+ years) and for the last 10 years have been getting some subassemblies made in China, Taiwan, Hong Kong.
The things I would watch for are:
Make sure the company communicates well in English. Many don't or they are so poor that one doesn't get anywhere. But to be honest, many Western firms cannot read or write either!
Make sure they talk straight, but see next point.
Be very courteous. In the West, if a vendor delivers a pile of junk, you can just email him and say something like "this is a pile of junk" or if you are polite you will say "the quality of the product is not acceptable". But if you talk this way to a Chinese man, he will take it as a personal insult and will never ever ever ever talk to you again, and the relationship with the company may be over. So one has to be less direct than with Western vendors.
The quality is whatever you want and want to pay for. The reason we see mostly junk come out of there is because most Western firms use the Far East to make the junk end of their product range, and make the better stuff locally to preserve local expertise, technology, vendor relationships, etc. The Chinese etc can make good stuff too.
Many firms out there don't make anything but resell stuff from down the road. This is a big problem; only a visit can make sure. If you get one of these, repeatability is an issue.
Getting stuff OUT of there is obviously easy but if you want to send stuff INTO say China (say some parts to do extra work on) this can get complicated. They have large scale corruption in their Customs, where an incoming package might cost $500 or whatever to get through. Hong Kong is OK in this case, IIRC, as is Taiwan, but China can be a hassle.
The bigger Western firms all second an employee out there, to smooth things, kick ass (very carefully) where necessary, etc. Not a bad job for a single man
Payment terms are normally 100% US$ in advance.
The only problem I have had, with ~ 3 firms out there, has been communication. Very recently, I asked them to label individual cartons (packed 90 per larger carton) and they did the right labels but stuck them on the larger carton, leaving the 90 inside unlabelled
The value for money and quality control which one can get out there is stunning and there is no point in going for the cheapest crap like nearly everybody else in the West does.
I send out populated and sample-tested PCBs out there, in 10k batches, and they package them in locally injection-moulded cases, 100% test them (using test equipment which I built and which we sent out there), package them, and return them by sea or air freight. The two kinds of freight are often similar cost.