All mnemonic escapes (character entity references) are case-sensitive, according to the standard. The official list of mnemonic escapes is defined here:
http://www.w3.org/TR/html401/sgml/entities.html
The organization, however, leaves something to be desired, being neither by value nor by coherent subgrouping (acutes together, or accented a's together, or paired characters together).

Here, I'm only concerned with which standard mnemonics are (and aren't) understood by Mudcat, though perhaps that may depend on the user's browser more than on Mudcat. With my browser (Firefox), I've found only a handful of oddballs.

The numeric escapes should always work, regardless of browser—as long as the defined character is printable and defined in the reasonably standard set of fonts. As it happens, values x80-x9F (decimal 128-159) are control codes in the Unicode map, so it's not surprising if they "sometimes won't work."

I should point out that mnemonic escapes are defined for a number of characters with values > 255; John's table is correct as far as it goes, but incomplete. In particular, there are mnemonics for most of the "troublesome" characters I mentioned, as well as for other quote symbols, currency symbols, a bullet, daggers, lone diacriticals, and additional ligatures and mathematical symbols.