QUOTE and DOUBLE-QUOTE encoding problems

I'm finding in some cases single quote is being displayed as (a-hat
followed by a char that looks like epsilon with 2 lines). These appear
to be ASCII 131 followed by 128.

Under linux, Mozilla, here is what I see:

A message comes in in GMAIL. I copy it to the buffer and paste it into
a textbox on another page. Oddly this step seem to change single-quote
from a small up and down quote to an extra-large curly quote. I try to
edit those out but don't always find them all.

I send the message to many users. On SOME systems, ie linux mail
client, the quotes all look fine. On others, instead of a quote, (a-hat
followed by a char that looks like epsilon) are displayed. There are
similar issues with double-quote.

Can anyone tell me how to avoid this?

Thank-You.