If the raw honey goes bad, how would I know?
What should I keep on looking for? Floating fungus?
Honey might go bad in two ways - one involves stuff growing on the surface of the honey, the other involves the honey itself fermenting. In both cases, the spoilage is connected to exceedingly poor storage - as other answers mentioned, honey is difficult to spoil... but difficult is not the same thing as impossible, right :)
Honey that ferments is usually linked to high water content - some honeys have a higher water content naturally, some might have water added at some point (for example, to deter crystallization), some might have water leaked into a container and puddled on top or along the edges, and honey will absorb moisture from the air if left unsealed, and eventually reach a saturation where the water is no longer a limiting factor to yeasts. In any case, part of honey's preservative qualities is the lack of available water and too high concentration of sugars inhibits most spoiling organisms - so when that extra water becomes available, honey turns from "never goes bad" to "potent food source for yeasts", especially since as the yeast eat the sugars, they also lower the concentrations from something inhospitable to yeasts, to something that can support more yeast growth - so the fermentation will continue progressing. A small puddle of water can gradually lead to a whole container fermenting because the local dilution is much greater than the total water percentage, and once given a foothold the yeasts will keep eating the concentrations further down into yeast-inhabitable ranges.
Some fermentation is more problematic than others - for example, mead probably originates from a spontaneous fermentation of honey that was enjoyable, on the other hand, different yeasts may give off bad odors and off flavors. If your honey has fermented to the point of spoilage, it will smell bad, look cloudy, and taste terrible. It will also foam (carbon dioxide production), may separate, may bulge if the container permits, all that good stuff that warns if any foodstuff in fermenting. There is some stuff on that page about natural beneficial fermentation and typical crystallization patterns, but that isn't relevant to the question of spoilage
The other way honey might go bad, is having some debris accumulate on the surface of honey (cross contamination), that gives some mold or other bacteria enough food to get a foothold. Again, honey itself is a poor source of food if properly stored - not enough water, not enough available food to get a foothold - but add debris, crumbs, or whatever that can spoil more easily right on the surface, and that can give mold or whatever enough of a toehold to build a floating colony, as you envisioned. If there's enough debris or moisture on the surface, the mold might start nibbling at the surface of the honey - which will start lowering the sugar content to something mold can find hospitable, much the same way fermentation can progress.
You might be able to simply remove the colony or even the top layer to salvage the honey, if you are willing to risk it, since honey is known to be rather inhospitable to dangerous organisms. And if the honey is properly stored afterwards, any critters left shouldn't be able to re-colonize since they needed the crumbs to get a toehold in the first place - but only you can decide what you will risk.
Heavy amounts of crystallization will show that the honey is old, but warming it will melt the crystals. Never seen it get fungus.
Well Honey is the only food that never goes bad, hence you will not find floating fungus like thing even after thousand year, actually raw honey is anti fungal. http://truththeory.com/2013/07/20/there-are-shocking-differences-between-raw-honey-and-the-processed-golden-honey-found-in-grocery-retailers/ above link provides you the difference between raw and processed honey.