offsetTop vs. jQuery.offset().top

I think you are right by saying that people cannot click half pixels, so personally, I would use rounded jQuery offset...

This is what jQuery API Doc says about .offset():

Get the current coordinates of the first element, or set the coordinates of every element, in the set of matched elements, relative to the document.

This is what MDN Web API says about .offsetTop:

offsetTop returns the distance of the current element relative to the top of the offsetParent node

This is what jQuery v.1.11 .offset() basically do when getting the coords:

var box = { top: 0, left: 0 };

// BlackBerry 5, iOS 3 (original iPhone)
if ( typeof elem.getBoundingClientRect !== strundefined ) {
  box = elem.getBoundingClientRect();
}
win = getWindow( doc );
return {
  top: box.top  + ( win.pageYOffset || docElem.scrollTop )  - ( docElem.clientTop  || 0 ),
  left: box.left + ( win.pageXOffset || docElem.scrollLeft ) - ( docElem.clientLeft || 0 )
};

• pageYOffset intuitively says how much was the page scrolled
• docElem.scrollTop is the fallback for IE<9 (which are BTW unsupported in jQuery 2)
• docElem.clientTop is the width of the top border of an element (the document in this case)
• elem.getBoundingClientRect() gets the coords relative to the document viewport (see comments). It may return fraction values, so this is the source of your bug. It also may cause a bug in IE<8 when the page is zoomed. To avoid fraction values, try to calculate the position iteratively

Conclusion

• If you want coords relative to the parent node, use element.offsetTop. Add element.scrollTop if you want to take the parent scrolling into account. (or use jQuery .position() if you are fan of that library)
• If you want coords relative to the viewport use element.getBoundingClientRect().top. Add window.pageYOffset if you want to take the document scrolling into account. You don't need to subtract document's clientTop if the document has no border (usually it doesn't), so you have position relative to the document
• Subtract element.clientTop if you don't consider the element border as the part of the element

Try this: parseInt(jQuery.offset().top, 10)