Looking for a Video Program/Feature that allows smooth frame-to-frame skipping (when moving progress bar)
mpv has very good real-time scrubbing using the mouse on the on-screen controls.

It also has seek-while-paused, and accurate-seek (decode-from-prev-keyframe) for seeking backward by 1sec.  Also frame-step backward and forward.  (controls: , and .).

It also has an A/B loop keybind, where you can easily get it looping over a part of the video.

So basically it has a lot of features that are great for reviewing a video frame-by-frame looking for problems, or stuff like that.

It's still in active development, make sure you get an up-to-date version for the most features and bugfixes.  I've only used it on GNU/Linux, but I understand it works on Windows and OS X, too.