If it works in emulators but doesn't work on real hardware; then the first things I'd suspect are:
bugs in physical memory management. For example, physical memory manager initialization not rounding "starting address of usable RAM area" up to a page boundary or not rounding "ending address of usable RAM area" down to a page boundary, causing a "half usable RAM and half not usable RAM" page to be allocated by the heap later (where it works on emulators because the memory map provided by firmware happens to describe areas that are nicely aligned anyway).
a bug where RAM is assumed to contain zeros but may not be (where it works on emulators because they tend to leave almost all RAM full of zeros).
a race condition (where different timing causes different behavior).
However; this is a monolithic kernel, which means that you'll continually be facing "any piece of code in kernel-space did something that caused problems for any other piece of code anywhere else"; and there's a bunch of common bugs with memory usage (e.g. accidentally writing past the end of what you allocated). For this reason I'd want better tools to help diagnose problems, especially for heap.
Specifically, for the heap I'd start with canaries (e.g. put a magic number like 0xFEEDFACE before each block of memory in the heap, and another different number after each block of memory in the heap; and then check that the magic numbers are still present and correct where convenient - e.g. when blocks are freed or resized). Then I'd write a "check_heap()" function that scans through everything checking as much as possible (the canaries, if statistics like "number of free blocks" are actually correct, etc). The idea being that (whenever you suspect something might have corrupted the heap) you can insert a call to the "check_heap()" function, and move that call around until you find out which piece of code caused the heap corruption. I'd also suggest having a "what" parameter in your "kmalloc() or equivalent" (e.g. so you can do things like myFooStructure = kmalloc("Foo Structure", sizeof(struct foo));), where the provided "what string" is stored in the allocated block's meta-data, so that later on (when you find out the heap was corrupted) you can display the "what string" associated with the block before the corruption, and so that you can (e.g.) list how many of each type of thing there currently is to help determine what is leaking memory (e.g. if the number of "Foo Structure" blocks is continually increasing). Of course these things can be (should be?) enabled/disabled by compile time options (e.g. #ifdef DEBUG_HEAP).
The other thing I'd recommend is self tests. These are like unit tests, but built directly into the kernel itself and always present. For example, you could write code to pound the daylights out of the heap (e.g. allocate random sized pieces of memory and fill them with something until you run out of memory, then free half of them, then allocate more until you run out of memory again, etc; while calling the "check_heap()" function between each step); where this code could/should take a "how much pounding" parameter (so you could spend a small amount of time doing the self test, or a huge amount of time doing the self test). You could also write code to pound the daylights out of the virtual memory manager, and the physical memory manager (and the scheduler, and ...). Then you could decide to always do a small amount of self testing each time the kernel boots and/or provide a special kernel parameter/option to enable "extremely thorough self test mode".
Don't forget that eventually (if/when the OS is released) you'll probably have to resort to "remote debugging via. email" (e.g. where someone without any programming experience, who may not know very much English, sends you an email saying "OS not work"; and you have to try to figure out what is going wrong before the end user's "amount of hassle before giving up and not caring anymore" counter is depleted).
