I'm using the Sampling generator and has you can see, for some reason, the little branches have these holes at the tips, why is that? And how can I get rid of them?
Use the Minimum Radius property under Branch Radius category to control the branch tip diameter while crating a new sapling tree.
You can also tick the option Close Tip as mentioned by Akados in the comments.
If you already created one then enter edit mode and select all branch tips and adjust their size with the Bezier Curve Radius property from the Properties Shelf Alt + S. You may want to turn on Proportional Editing
To easily select all tips you may use the Select Grouped operator with Shift + G and try to select by Radius.