I will absolutely recommend testing the ROM/PROM/FLASH after programming (most parallel programmers do it unless you tell them not to) using the means of programming (ISP code/programmer) to do so. I do not believe that testing ROM after that serves a useful purpose.
The example of memory timing problems discovered by a memory test is just an example of bad design (too close to tolerance). If you do some "strange" memory access, write a snippet to test your design, do not write to test memory.

Erik