ZEsarUX:known bugs

You may want also to check the official ZEsarUX FAQ to see if you have a known issue which has solution (ZX Next is "TBBlue" type of machine).

Official ZEsarUX 8.1:

sprites rendering is at "4B type" level (no anchor/relative sprites or scaling) (5B init is correctly accepted but doesn't render the extra features)
4bpp sprites are not supported
sprites rendering is not one-scanline-buffer delayed and all changes in sprites affect current scanline
Layer 2 displays shadow variant (NextReg $13) when the "shadow" mapping is enabled
Layer 2 modes 320x256x8bpp and 640x256x4bpp are not implemented
Layer 2 extra memory mapping controlled by Layer 2 Access Port ($123B / 4667) works only in core2.x way.
modifications to NextRegs done in copper propagate to rendering usually only once per scanline, usually retroactively for full scanline when triggered in h-blank area (palette changes, X/Y offsets, etc)
palette read (NextReg $41 + $44 produces wrong results)
tilemode gfx/map address read (NextReg $6E + $6F) does return original value without top bits set to zero
DMA: too many differences to list, but most crucial: CONTINUE is not supported, slow "burst" functionality is not complete, legacy Z80 mode is not implemented
blending modes are not implemented
ULA scroll is not at new NextReg $26, $27 (but still shared with LoRes offset registers)
audio has "clicks" and noise on many platforms, although YMMV
monochrome tilemode has not fully correct colours handling
tilemode doesn't wrap in memory the same way as HW (when gfx/map address is toward end of Bank 5)
direct loading of NEX file doesn't init the machine in the same way as NEXLOAD from NextZXOS (it's close, but few things are different)
screen saver of NextZXOS will "crash" the emulated machine (not emulator itself)
when running without the full NextZXOS card image, the esxdos services are provided by the emulator itself, which does not implement all of them, and they don't always return the state described by the NextZXOS documentation

Already fixed in git (but present in 8.1. release):

altROM next register does not work correctly and core 3.1.3 does further change it

Other Issues (not a bug):

28MHz mode requires quite powerful PC to emulate it smoothly, "lagging" emulator menu/etc is likely to happen in 28MHz mode and unfit for many development purposes.

Personal "ZESERUse" fork of Ped7g:

modifications to NextRegs done in copper propagate to rendering usually only once per scanline, usually retroactively for full scanline when triggered in h-blank area (palette changes, X/Y offsets, etc) - when compiled with extra flag "-DTBBLUE_DELAYED_COPPER_WAITS" it will delay copper instructions waiting for h-blank till next line (does produce better visual output in some cases, but makes the emulation less accurate in terms of timing)
altROM/global memory map not updated to core 3.1.3 changes
audio has "clicks" and noise on many platforms, although YMMV
28MHz mode requires quite powerful PC to emulate it smoothly, "lagging" emulator menu/etc is likely to happen in 28MHz mode - the fork is even more power hungry than official version
blending modes are not working, missing core3.1.3 features completely, core3.0 is implemented code but broken in current version
sprites rendering is not one-scanline-buffer delayed and all changes in sprites affect current scanline, calculation of pixel-bandwidth exhaustion is vastly incorrect
tilemode doesn't wrap in memory the same way as HW (when gfx/map address is toward end of Bank 5)
screen saver of NextZXOS will "crash" the emulated machine (not emulator itself)
when running without the full NextZXOS card image, the esxdos services are provided by the emulator itself, which does not implement all of them, and they don't always return the state described by the NextZXOS documentation
DMA should have two ports since core 3.1.3 and the legacy/next mode depends on port number, not nextreg $06
missing Nextreg $8E Spectrum memory mapping (core 3.1.3)