Occasionally, checkers just moved are not rendered at all until another checker is moved on that point.
Likewise sort of ghosts like half-checkers of checkers already moved remain on the points until that point is populated again.

Environment:

JavaFibs 1.012/JavaFIBS-1.0.12_java16.jar

run with

java version "1.7.0_75"
OpenJDK Runtime Environment (IcedTea 2.5.4) (7u75-2.5.4-2)
OpenJDK 64-Bit Server VM (build 24.75-b04, mixed mode)

or

java version "1.8.0_45"
Java(TM) SE Runtime Environment (build 1.8.0_45-b14)
Java HotSpot(TM) 64-Bit Server VM (build 25.45-b02, mixed mode)

on

Linux ... 3.16.0-4-amd64 #1 SMP Debian 3.16.7-ckt9-2 (2015-04-13) x86_64 GNU/Linux
NVIDIA X-Driver 340.65

Thx, @diane!

I am afraid at this time, you will just have to live with it - [...]

Maybe not.

Such presumably redraw-event/blending/depth related errors are a very common symptom of certain class of applications, and there is a chance that running the jvm in a specially tailored environment would help avoid the symptom in a non-intrusive way, which appears with this

but work on javafibs has fallen to the wayside due to extreme difficulties with obtaining permission to meddle from the author.

in mind the most appropriate, if not only, course of action anyway.

But first I'd need some more detailed log to validate my hypotheses -  do you know by chance a command line or config switch to get that app logging extensively, or even sort-of tracing?
The included "help" content is not especially verbose about this, to say the least.   

With kind regards,
D.