tikki,
I've taken a quick look. Gecko rendering and ie-mac rendering look pretty similar to me

Camino

Mac IE
Looking at the html though, you've used an id of form twice, ids should only be used once, i.e using ids for right and left colums makes sense. However, your stylesheet uses classes, so I don't see why you got both ids and classes of rightcolumn, leftcolumn.
Personally i'd change it so the header, and column divs all use ids.
Then there are a couple of options on positioning.
1) Relative positioning
Code:
#leftcolumn {
position: relative;
top: 10em;
float: left;
left: 0px;
width: 50%;
}
#rightcolumn {
position: relative;
width: 300px;
margin-left: 50%;
top: 10em;
}
.header {
position: relative;
top: 0px;
width: 80%;
text-align: center;
margin-left: auto;
margin-right: auto;
}
Play about with widths, padding and margins. etc. I'd personally use ems for positioning and text so if anyone changes the size of their text everything stays nice
Here the width of the left column is set and the right hand column moved over by that width using margin-left. The left hand column is floated
2) Absolute positioning
With this floats aren't necessary. Specify it something like this:
Code:
#leftcolumn {
position: absolute;
left: 0px;
top: 10em;
}
.header {
position: absolute;
top: 0px;
width: 100%;
text-align: center;
left: 0px;
}
#rightcolumn {
position: absolute;
top: 10em;
right: 0px;
width: 310px;
}
This seems better since the size of the right hand column is set and eveything else is fluid from that, i.e everything is driven from the right hand side. Although theoretically possible to achieve with floats and relative positioning it's probably harder to do.
Hope this is some help.