Sketchy company - should I change jobs before my Visa goes through?

I am looking for any helpful advice on my position. I am currently working for a company here in Qatar (4 months now) and am concerned about how the company operates and runs. My position is not at stake in any way, however, I have been feeling it is a poorly run and organised company to work for. I don't have a Visa yet, my salary is always late, the "temporary" car I was given upon my arrival I am still driving, and has broken down 4 (yes 4!) times, and finally today I refused to drive it anymore after another breakdown. They don't care about providing my department with the right equipment and support to do our jobs. These are just a few issues. I have been advised a visa has come through for me this week, so they will start the full application process to organise the blood test etc.

I have an opportunity to work for a world renowned company here also, if I felt I should change jobs.

My question is should I begin arranging a new job or stick out this current situation and get the visa with my company? Would I be better to get out now before I am "locked in", so to speak?

Thanks for your suggestions and advice.