It looks like only IE8 reads your code for that border. Firefox, Opera, Chromium, and Safari don't get it. Browsers display the authors intentions better when the coding used is valid.
http://validator.w3.org/check?uri=http://www.cbrundage.net/cleeve/nature.htm
Browsers are displaying that page in the Quirks Mode.
http://en.wikipedia.org/wiki/Quirks_Mode

See this for help with the code you are using.
http://www.w3.org/TR/CSS2/box.html#border-properties

If you need more help with that issue, try posting at the Web Development / Standards Evangelism forum at MozillaZine. The helpers over there are more knowledgeable about web page development issues with Firefox.
http://forums.mozillazine.org/viewforum.php?f=25
You'll need to register and login to be able to post in that forum.

You have a spurious } in your CSS code, just remove that line and it should work.

a:hover {color:#E1E0AF}
}
table.mytable {

a:hover {color:#E1E0AF}

table.mytable {

^ Good catch. There's another spurious closing bracket 6 lines below the one you found.

background-color:#e8e5da;}

That is not a spurious } , but a needed one to end that rule.

table.mytable {
 border-width: 6px;
 padding: 15px;
 border-style: dotted;
 border-color: #88aa96;
 background-color:#e8e5da;
}

.back td{
 background-color:#e8e5da;
}

img#bg { .... }

Thank you all so much! That solved the problem - I really thought it was a browser problem!!! Christina

You need that } after background-color:#e8e5da;

By removing it you introduced another error:

Warning: Expected declaration but found '.'. Skipped to next declaration. Source File: http://www.cbrundage.net/cleeve/nature.htm Line: 33

table.mytable {
border-width: 6px;
	padding: 15px;
	border-style: dotted;
	border-color: #88aa96;
	background-color:#e8e5da; /* missing } /*

.back td{background-color:#e8e5da;
	}

Instead of background-size you probably mean background-position:

Warning: Unknown property 'background-size'. Declaration dropped. Source File: http://www.cbrundage.net/cleeve/nature.htm Line: 15

background-attachment:fixed; background-size: 100% 100%;

I put the "}" back but it had worked anyway and the background stayed fixed too. But thank you for getting my coding fixed! I really appreciate it. Christina