I'm pretty sure the warnings and errors are not being caused by WP-Juicebox.
It looks like WP-Juicebox is just being caught up in the mix.
Maybe you could create a couple of new WordPress installations on your web server alongside your existing one but essentially just for testing purposes (with addresses that no-one would know about).
You could install and activate WP-Juicebox in only one and keep the other as a control.
Try creating a few galleries (in the installation that you have installed WP-Juicebox into) and tests posts (in both) and check your web server error log after a while of testing and using both new installations.
If you see no errors at all relating to either of the two new WordPress installations, then the problem is likely to be due to your original WordPress installation.
If you see errors relating to both new WordPress installations, then the problem is likely to be due to your web server.
If you see errors relating to only the new WordPress installation that you have installed WP-Juicebox into, then the problem is likely to be due to WP-Juicebox (although I think that this is very unlikely).
I realise that this will require a bit of work and your new WordPress installations will not get any traffic other than your own testing (which will result in less warnings and errors in the log) but it might help to track down the cause of the problem.
Since installing juicebox we are getting a lot of intermittent Server errors on our web site.
I think the clue here is the word 'intermittent'. The code on your web site does not change and should give consistent results. If there is any inconsistency, then it could certainly be due to server problems.