There are a few sequences from the 2nd TV series 
that are unusually well done (and look quite a 
bit nicer than the 1st TV series and scarily 
close to OVA/movie quality) and would go pretty 
high on web sites/auctions.

The origin sequence from Ep. 7 (not Ep. 8) where 
the girls meet Tenchi for the first time.  You 
can pretty much tell where most of the budget 
went into for the beginning of the 2nd TV series.

The battle sequence with Yugi from Ep. 13.  In 
particular, when Yugi shoots a beam through 
Ryoko's throat.  (This is about when the series 
started to shift into a more serious mode.)

Episode 20 in general.  If only the entire series 
were animated like this episode. . .

Yugi's origin sequence on Jurai.  Forgot which 
episode (21?).  At first, it seems like you're 
not watching the series at all, but some other 
anime.  Of special note is Queen Hinase (Maybe a 
long lost relative of Lady Tokimi, heh.)

Of course, there are some other nice spots 
throughout the series, but those seem to come to 
mind quickly.

(Cel below is from the final episode. I guess 
it's not often when you see those two together 
being sincerely happy, heh.)