An "Help" button would be a good idea (easy to implement since F1 provides help).

A very confusing thing is the use of "set" and "subset" in the same window,
while the subset is not a subset of the set. The fact you can decide to call
"phi" a theta, for instance, is also confusing. So I suggest that you
distinguish very well editor features from official nomenclature:

1) Unicode number and official name of both old and new symbols could appear
under the two big symbols (right bottom of the window), and labeled "official
number" and "official name", respectively.

2) It'd be clearer if "Old Symbol" was renamed "User old symbol name",
"Old symbol set" would be renamed "User old symbol set";
"Symbol" would be renamed "User symbol name",
"Symbol set": "User symbol set";
"Subset": "official subset".

3) under "official subset", an "official character name" could appear,
giving the ability to choose from the Unicode subset, or, at least, to see the
name of the selected character. Some characters are very similar, for instance a
Lucida sans greek chi looks like x, an upperlined cyrillic h looks like Planck's
constant symbol, zero looks like O, a cyrillic capital A is exactly like a latin
A and like a capital greek alpha etc. This is why the name is important.

I suggest "Editor old symbol name" and "Editor symbol name" are placed after
"User old symbol set" and "User symbol set" fields respectively, since symbol
list depends on the set.

A bold broken line could delimit, in the character table, the selected subset.

The part of this window aiming at selecting a new character and the Writer's
Special characters window should be identical.