One is texture compression, as I just mentioned. As long as the hardware needs DXTC, there's really not much I can or *should* do. I'd have to decompress then recompress to DXTC which is just pointless. Stop thinking about it.
Another is antialiased rasterization. Particularly in LRB I think you could do a pretty sweet exact antialiased rasterizer. But it's pretty pointless for 3d. It might be nice for 2d, for fonts and vector graphics and such, but in 3d the bad aliasing isn't even because of edges. The bad aliasing comes from various things - mainly failing to filter textures well when they aren't plain color textures (eg. mip-mapping normal maps), or aliasing due to lighting, and especially reflections (BTW specular is a type of reflection). Fresnel specular reflections are the worst because they're strong right at edges where you have very little precision, so they sparkle like crazy. To really handle these cases you need something like adaptive super-sampling (putting more samples where you need more detail). And to really do that right you need your shaders to return frequency information or at least derivatives.
... but I'm not thinking about that any more because it's pointless.
Oh and I should mention some other things about texture compression while they're in my head.
1. While the fixed block size is really bad for RMSE, it's not quite so bad for perceptual error. What it means is that you put "too many" bits in flat areas and send them almost perfectly. In noisy areas you don't have enough bits and send them very badly. But that's sort of what you want perceptually anyway. It's not actually ideal, but it's also not horrible.
2. One thing that none of these formats do is take advantage of mips. Assuming you always have a full mip chain, and you're doing trilinear filtering - then any time you need mip M the hardware already have mip M-1. Obviously you could do very good delta compression using the previous mip. For something like paging the situation is a little different, but you could certainly require that you have the 16x16 mip always in memory and at least use that for conditioning. I haven't really thought about this in detail, but obviously sending a whole mip chain without using the information between them is very wasteful.