There are only a handful of particular cases where PCI-E 2.0 graphics card would not work on a motherboard with a PCI-E 1.0 chipset, and it was more of an interoperability issue, not a "compatibility" issue. This was almost exclusively limited to VIA chipsets and a cohort of older NForce 4 motherboards with a buggy BIOS.
There are cases involving older motherboards based on Intel 915 and ATI RS482/485 as well, but this only affects the HDMI audio controller that is integrated on newer PCI Express graphics cards (e.g. Radeon 3000 and higher, GeForce 9 and higher), not the actual graphics. IOW, the graphics work fine, only the onboard HDMI audio controller won't function.
Other than that, there are no problems.