I thing where Windows 98 fall unstable is in 2 sections.
1) Memory - Windows 98 does not use its memory/resources/etc sufficiently. Most BSODs can be fixed by upgrading (in Win98 to more memory). This problem comes from having to go to the paging memory as opposed to hardware memory.
2) Driver handling - Poorly written drivers for the Windows 98 OS have caused a lot of problems.
These two things give the illusion that Win98 is unstable.
If anyone wants to talk trash about instability... go out and install Windows ME and then come back.