Use case: removing filler words from a screencast / speech etc. while there's a slide displayed, so there's no video discontinuity.

These two tickets show how cumbersome the process is.
http://www.kdenlive.org/mantis/view.php?id=2681
http://www.kdenlive.org/mantis/view.php?id=3137

In Lightworks, this is very simple - it's what "Delete" does. ("Remove" does what "Delete" does in Kdenlive.)

Is there an easy way to remove unwanted portions of a video, and fine-tune the removal start & end when necessary?

there's currently no 'ripple delete' functionality in Kdenlive ('ripple delete' is what it's called in Final Cut).
This is the quickest method I've found (still slow compared to proprietary NLEs).
let's say we want to remove 'DE' from the following clip:

ABCDEFGH
Navigate (use J, K, L) to D
Click the track(s) you want to cut
Shift+R to cut
Navigate (use J, K, L) to F
hit 1 to set clip DEFGH's In Point to the current frame (F)
ABC FGH
hit your shortcut for the 'spacer' tool (mine is set to T
Click in the gap and drag everything to the left.
ABCFGH

it's faster than messing about with the scissors tool, but a lot slower than traditional 3-point editing in the timeline, which in FCP is just:
ABCDEFGH
Navigate (use J, K, L) to D
I to set In Point
Navigate (use J, K, L)to F
O to set Out Point
Delete/Remove to Ripple Delete.
ABCFGH