If the 68030 is in use, then perhaps you've accidentally installed drivers or software that requires 68040 or 68060. In the worst case, the disc and software have simply been damaged.
The 68040/68060 didn't introduce any new integer instructions except MOVE16 which I have never seen a compiler generate. There are new FPU instructions like the FSxxx and FDxxx but I believe they would give a different guru number. Sometimes users with a 68020/68030 and no FPU will accidentally install FPU versions of software but I didn't think was the case here.
It could be some kind of problem with the reading or formatting of the HD. SFS can cause problems, a mildly corrupted file system or HD, weird HDToolbox settings, partitions >4GB, etc. It could just be a bug triggered by certain settings or hardware. The Cache CD-ROM system is less than robust. Some MUI classes and datatypes are buggy as well. It would probably be good to disable programs started at boot and see if the problem goes away. It would be nice to know the name of the offending program but the SegTracker+SmartCrash software is technical and may not work if it crashes hard.