The biggest problem with x87 is basically that all register operations are done in 80 bits, whereas most of the time people only use 64 bit floats (i.e. double-precision floats). What happens is, you load a 64 bit float into the x87 stack, and it gets converted to 80 bits. You do some operations on it in 80 bits, then store it back into memory, converting it into 64 bits. You will get a different result than if you had done all the operations with just 64 bits, and with an optimizing compiler it can be very unpredictable how many conversions a value might go through, so it’s hard to verify that you’re getting the “correct” answer when doing regression tests.
The other problem, which only matters from the point of view of someone writing assembly (or indirectly writing assembly, in the case of someone writing a code generator for a compiler), is that the x87 uses a register stack, whereas SSE uses individually accessible registers. With x87 you have a bunch of extra instructions to manipulate the stack, and I imagine Intel and AMD would rather make their processors run fast with SSE code than trying to make those extra stack-manipulation x87 instructions run fast.
BTW if you are having problems with inaccuracy, you will want to take a look at the article “What every programmer should know about floating-point arithmetic“, and then maybe use an arbitrary precision math library (e.g. GMP) instead.