Explain unusual stability of chloral hydrate.

Chloral hydrate is stable not so much because the geminal diol is stabilized, but because the aldehyde form is destabilized as compared to, say, acetaldehyde (which also hydrates reversibly in acidic aqueous solution). The sp2 hybridized carbon in the aldehyde is very electron deficient, so it reacts with electron-rich nucleophiles (like water). Acetaldehyde, with a methyl group, slightly reduces the electron deficiency by "donating" some electron density. Trichloroacetaldehyde, however, cannot donate nearly as much electron density because the electronegative chlorine atoms are pulling electron density away from the already electron-deficient carbon, making it even more reactive.

Formaldehyde, like trichloroacetaldehyde, exists primarily as the diol form, and even oligomerizes and polymerizes with itself in the absence of water (1,3,5 trioxane and "paraformaldehyde"). Here the issue is not electronegativity (the hydrogen substituents are fairly electron-rich, and energetically favorable to share). Unfortunately, there is a symmetry mismatch in the orbitals involved, so it is impossible for the hydrogen substituents to ease the sp2 carbon's deficiency. Therefore, formaldehyde reacts with water, alcohols, proteins, even itself, to relieve the strain.