Hiya Lewis,
there are a number of reasons why this is happening right now. given similar problems were being reported in the il2 days, the most likely answer is that it is due to errors in LoD modeling of some aircraft in CoD.
this would mean that it is unlikely to be addressed untill the new gfx engine is completed (luthier prev stated this engine rebuild would be provided a couple of months before xmass, but it keeps being delayed with no reasons given as to why), since they will first try and get the scenery and gameplay right before they try and fix "minor" design errors in objects.
there is an interesting dicussion on some of the object visibility problems in CoD here:
http://forum.1cpublishing.eu/showthread.php?t=27410
if however you and your team mate see these distant objects differently from the same viewing position and distance (and both use a "correct FoV" setting for your monitor sizes, eg that the other person doesnt use a zoomed view), then it might not be a defective LoD model. can you plz state what monitor you and your team mate use ? (brand and exact model type plz). i suspect you have an 8 bit colour monitor, and your team mate might have a 6 bit monitor. the cheaper 6 bit colour monitors have display artifacts (which is usually bad news and degrades the quality of the video image), but those same artifacts make small black/grey dots stand out more (which in il2 and CoD would make these distant aircraft dots easier to see). this was a major isssue in il2, but was only identified as an issue late in the il2 series.
the sugestion Gratos made earlier in this thread ( MeshShowLod = 1) is a very nasty and ugly hack that is unlikely to solve the problem, and will significantly slow down your fpsec's (there are older threads in this forum on that hack). also having to revert to il2 settings from 1999 and use "Resolution 1024x768" is rather barbaric and self defeating because the rest of the game becomes so ugly.
solutions imo should instead be focussed on identifying the exact cause of the problem (which is a game design bug/error) and then fixing the problem, not using workarounds that are inefective and ugly.
did you keep the track you recorded ? (which you posted the video from). try and use a zoomed external view in slow motion that focusses the camera on the disapearing object, and see what exactly made it go invisible (eg does the LoD model show defects when it transitions from one to the other).