First off, Gigabit Ethernet was designed to run on
Cat5. Cat6 is future-proofing. So if you have problems with the cables, it's more likely due to a physical problem than not having Cat6 cables/jacks. Often the jacks will say what they are rated. The only way to see what the cable is, is to open a wall plate and look at the cable.
A real network installer should have a high end tester that can check the quality of the connections. I know I've seen a keystone jack that failed end to end testing, even after repeated punch downs, so I tossed the jack. Another jack from the same box tested good. A cheap wire map tester would have passed the defective jack. A reputable installer will want you to be happy with the work, have you contacted them?
I think the real question should be, "how can I tell why the connection between point A and point B are not what I expect?". With a description of what point A and B are, the physical path it travels, and any equipment in the middle.