Generally you're looking at a couple of things that can cause this ('dots on screen conversations above'). I'll break down what I've seen personally in my experience across different cams and manufacturers below, and ways in which I have personally mitigated the issues if I see these. The algorithm related one is very much more prominent on full color cams based on tech being used and the AGC processing being used to bump the performance or output from full color cams at night.
1 - Algorithm Related - Due to the tech employed by the algorithm itself on full color cams you do see digital elements such as the white dots on these full color cams in very dark or pitch black areas. Testing for this would be to raise exposure super high during the day and/or at night (basically creating a very dark scene), look for where the identified dots show up and see if they're static (never move on screen). If you see them 'sparkling' and / or if you see them change position on screen within the FOV, this is generally algorithm related.
MITIGATION - Can be mitigated by reducing gamma (in my experience try 35-40) when in brighter night FOV's, or by increasing light on scene in darker night FOV's and reducing gamma just slightly, say 45. The combination of both should assist along with reducing gain, try dropping 4 points so 0-45 first and see how you get on
2 - Digital Noise Related - Generally seen as crawling or pulsing, depending on where it's seen on screen may appear bright or dark
MITIGATION - Can be mitigated by increasing noise reduction (do it gradually and certainly for night would try and stay around 40) and / or reducing gamma (similar to above, I would try between 35 to 40)
3 - Dead / stuck / hot pixels on Sensor - Can occur but is usually limited by batch and if spotted (and aren't tons of them on screen) can be resolved - Generally can be identified by super high exposure during the day (again creating a dark FOV) or of course by waiting for night and again increasing exposure until dark enough to see black screen (prefer this to covering the lens) and see if you see the pixels show up AND critically if they are in the same place each time (screen grabs from each are good for a before / after).
MITIGATION - You can usually resolve these (again assuming there isn't a ton) using Pixel Mapping.
@CCTVCam believe this is what you were referencing as well. Absolutely the can be done. This is generally done at a factory (if noticed on batches in production and not related to a larger issue) but can be completed with FW tuning as well. Basically the FW will look for and identify defective pixels. It then marks these and can ignore or work around them. It does all of this by calculating the data captured by other pixels surrounding defective ones. In registering these it 'tunes' or eliminates those used.
MITIGATION 2 - Another mitigation here so they are not as prominent seen is to again reduce gain BUT critically only by small amounts as you don't want to ruin your capture. Therefore in a well lit night FOV consider dropping to 0-30 but I wouldn't push down any lower than that. You can also adjust noise reduction up a little to see if that assists (again can assist in making them less prominent) but no than to 42 or so, again don't ruin your overall image
4 - Dust / Contaminants On Sensor - Will generally show as blurred areas of the optic itself and impacting the image rather than just bright white dots present on screen.
MITIGATION - Inspect the overall lens optic for opportunity to clean BUT if this is inside the sealed unit only a replacement would resolve this
With ALL of what I said above, for
@BadKarma above with these 'moving around', this looks more to me like the Algorithm Related piece I mentioned above in my experience. Settings can assist here for sure in terms of mitigation.
@BadKarma feel free to DM me each settings page and a) I'll mock up your settings and then b) recommend what I feel you should have yours set for and you can then retest. I can also jump on your system and dial in so we can take a look together if you wish
HTH everyone