I'm rebuilding a three-year-old AMD Athlon 5000 system which has an "ASRock NF7G-FullHD" motherboard with 4 memory slots, labeled "DDR2 800", said to have RAM capacity 8GB total. Besides 550W PS and 500GB disk I bought a "matched pair" of 2 ea. 2GB DIMMs that, unfortunately, have persistent single-bit errors at several locations (see picture).
What would be the effect of running Linux on this system with such memory? I.e., how likely is instability, undetected error, or low performance? Will there be OS crashes, segfaults, miscellaneous application failures, or what? Is there a way to map out or disable bad chunks of RAM?

Note, the 4 memory slots are labeled DDRII_1,2,3,4; 1&2 are yellow, 3&4 are orange. The Memtest86 picture above was taken when slots were filled in (new,old,new,old) order. Errors also occur at similar addresses with fill order (old,old,new,new), with same memory access rate (about 2.9GB/s) as in picture. Filled (old, old, -, -) or (old, -, old, -) or (new, -, new, -) no errors occurred in a few hours of testing, but (new, new, -, -) for some reason didn't get into or through BIOS and reset button appeared to have no effect and there was no video signal. With 3 slots filled, e.g. (new1, old, new0, -) one error occurred (located in first GB of RAM) in 1.5 hours of testing; with (old, old, new0, -), no errors in 2 hours of testing. A performance problem with 6GB configurations is memory access rate of only 1.7GB/sec.
Question summary: What would be the effect of running Linux on this system with memory subject to some single-bit errors? Is there a fix other than replacing RAM?