What nutrients can humans absorb in the mouth?
Quite a bit can be absorbed through the mouth. Most commonly, starches are broken down to maltose (two glucose molecules formed by a condensation reaction) and are easily absorbed by the bloodstream. 

A lot of other factors balance into this, ie pH, lipid solubility, and molecular weight. Generally, if a substance is easily dissolved in saliva, it can be administered buccally or sublingually because the only remaining step is the diffusion into the subepithelial capillaries. In regards to speed, anything properly absorbed via buccal or sublingual administration goes to work much faster than a standard oral medication, and with a higher availability in the bloodstream. You are taking first pass metabolism and enzyme breakdown in the stomach out of the equation by diffusing the drug directly into the bloodstream.

There is quite a laundry list of medications that can be administered transbucally or sublingually, just a few of these:
Nitroglycerin
Acetylsalicylic acid (aspirin)
Glucose gel (as you mentioned)
Fentanyl (a narcotic painkiller)
buprenorphine (for opioid dependency)
Benzodiazepines (alprazolam, clonazepam)