Polylines meet with IE but not with Firefox?

I am fairly new to this, so I may well have missed something.

I am trying to produce a map of a tour of Central and South America I
plan to take. I intend to upload GPS tracks as the trip progresses. At
the moment I have my intended route displayed as a series of polylines.
At one point I have three lines that meet (at Manaus in Brazil).

See http://www.xor.org.uk/silkroute/panam2006/googlemap.htm

If you zoom in on Manaus (the yellow dot in the middle of Brazil) the
three lines converge at all magnifications in IE but if you use Firefox
then when you get to a scale of 5 miles/5 km the three lines no longer
meet.

Can anybody help me understand why?

Stephen Stewart