Introduction
Several of these 'incidents' were not jDownloads related 'challenges' but due to things outside jDownloads but they may appear to be a jD problem!
As other such problems are found then they will be added to this article.
Check Download Area not working
Example plugin activated
Admin Tools causing 403 Forbidden
If you have used Akeeba Admin Tools to create your .htaccess file then you will find that you get a '403 forbidden error.
It seems that Admin Tools does not allow spaces in Directory Names.
However, because the directory name cannot have spaces in it, this means that jDownloads category names cannot have spaces in them!!
As a result of this 'function' of Admin Tools, any .htaccess file created should not be used on any website with jDownloads.
Even if your site does not presently use 'external files', one day you might start using them. You would then perhaps blame jD exernal files capability!!
Front End seems slow
Most of the Downloads were unchanged. So it seemed a possible solution was that increasing the cache size might help. But this did not solve the problem. And in any case increased cache size does not help first time or occaisional users.
The site had high security and was using IP blocking with Akeeba Tools. Now that meant extensive IP checks were being done on every page load. As it was the Downloads that really needed the protection then the IP blocking was switched to the jDownloads option 'Activate IP Blocking' in the Options tab Security. This IP blocking only operates when attempting to download a file.
This also speeds up the general switching between jDownloads views say from a Downloads Listing to a Downloads Detail or Summary view.
So speed problem solved and security maintained.
Downloads slow to Start
One maybe that the Joomla Error log file is very large
The other is that jDownloads database logs table may be very large.
Joomla Log Files
jDownload logging
In the jD 4.x series the jD System Plugin has the ability to limit the size of the log file.
It is not limited by the number of entries but by a duration of 93 days. The value of 93 days is the maximum length of a 3 month period.
This duration is because jD can set a monthly limit on the number of downloads by user group members. So jD needs a suficiently long log file to enact the limit properrly in all situations.
In earlier versions the default setting of this parameter, which is "How long, in days, should the rolling period for keeping download logs be?", in the System Plugin was zero which meant no actual limit in size. So if you upgraded from jD3.2 or from early versions of jD3.9 then it would have used the existing setting of zero meaning there is no database limit!
To check the setting in the jD system Plugin goto Extensions and select Plugins as indiated opposite.

And then click on the Search Button
Then Click on the System - jDownloads to open it up to see the options.
.

If you are using the jD Usergroup 'Limits' then ensure it is at least 93 days.
Otherwise set as you requie but it is stongly suggested that you do NOT set to zero.
Setting zero does NOT turn of the recording of each Download!

Where does jDownloads select font Colour?
jDownload Category List View seemed to only appear once!
This sort of symptom is consistent with having caching active. It could be the Joomla cache, or perhaps the Browser cache. But clearing those caches may not solve the problem!
Some web modems, particularly those working with a satellite, also have a significant cache. So it may be necessary to reboot your web modem in order to clear its cache.
Old Items -maybe fixed
Error 500 after updating
Invisible Cats or Downloads
This looked like it was a view Access level or possibly a Permissions problem. But no, all was well on those fronts.
But even the super user could not see, even when added to every view Access level. The problem was traced to the ECR plugin (this is not Easy Content Reader but Easy Content Restriction).
The plugin, which is embedded in the articles, is very flexible. It works by requiring a password associated with the article or by blocking specific usergroups to see the content. But this is not compatible with the jDownloads.
Disabling the Plugin resolved the problem.
UPDATE It is understood that an updated plugin is available from the ECR developer.
Green Bar on Video Images
Usually this is with a Firefox browser.
See https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems (opens in a new window/tab)
for various causes/solutions.

After turning off hardware acceleration the green band problem was fixed and colours were back to normal.

The DP Calendar Extension
However sometimes this goes wrong!
Investigation determined that problems only occured when the content plugin was added for a Download in the first line of the Description.
So a line like below where the content plugin, which has been slightly highlighted for clarity, is in the first line of the DP Calandar description:
"Here you may download additional information
will cause 'challenges' with symptons such as other modules 'vanishing' and no further calandar events being shown.
However if the DP Calendar description is in the second or subsequent line as below:
"You will find some additional information
by clicking on the download
All then works OK
NB the DP Calendar people are aware of this 'challenge' so it may have been fixed.
