http://www.littlegolem.net/jsp/game/game.jsp?gid=1478338

In these game there are 3 empty spots left. These were the spots where noone could put a piece. Is this a bug, or is it an obscure rule that none of us know about?

No bug at all. It seems you are both missing one of the core rules of Slither. When it's your turn, you do TWO things:

1) MOVE a stone (optional)
2) Place a new stone

This is very essential. Only in very few situations do you not wish to move a stone. In your situation, placing a stone would have been possible if you first had moved a stone.

Hint: Look at a game between top players to see how the game should be played :-)

Indeed, moving is a vital part of the game. It's what gives slither a unique twist, and its name.

In a situation like yours where you've got alternating colours on two sides of a gap, out of phase, such as

xox
---
oxo

You can typically move one of the pieces …

-ox xox
-X- or X–
oxo o-o

and then place the necessary connecting piece

-ox xox
-xX or x-X
oxo o-o

(And let's hope the tags work…)

Thanks, both of you. We're new to the Slither, and I guess we may have missed a few details about the rules of the game.
Think we were a bit too much stuck up with the rules of Hex and Twixt to see the difference.
Thanks again. :)