QUAKETALLICA: Hi, I was having this problem as well after a recent Windows 10 update (from version 1909 to 2004).
Thanks a lot for your fix! It worked for me. Installing a Reshade/SweetFX is entirely unnecessary. However, following the PCGamingWiki's instructions on creating an autoexec.cfg, copying that block of text in, and changing r_subdivisions to 3 did the trick! Thanks for sharing this solution.

In case anybody else has this same issue in future, go to your game directory/main (or mainta or maintt for the expansions). Then create a new text file and rename it to autoexec.cfg. Then copy the following in and save the file:

seta cg_drawviewmodel "2"
seta cg_effectdetail "1.0"
seta cg_marks_add "1"
seta cg_max_tempmodels "1200"
seta cg_rain "1"
seta cg_reserve_tempmodels "240"
seta cg_shadows "2"
seta g_ddayfodderguys "2"
seta g_ddayfog "0"
seta g_ddayshingleguys "2"
seta r_colorbits "32"
seta r_drawstaticdecals "1"
seta r_ext_compressed_textures "1"
seta r_fastdlights "0"
seta r_fastentlight "0"
seta r_forceClampToEdge "1"
seta r_lodcap "1.0"
seta r_lodscale "1.1"
seta r_lodviewmodelcap "1.0"
seta r_maxmode "9"
seta r_picmip "0"
seta r_picmip_models "0"
seta r_picmip_sky "0"
seta r_subdivisions "3"
seta r_texturebits "32"
seta r_texturemode "GL_LINEAR_MIPMAP_LINEAR"
seta r_vidmode1024 "0"
seta r_vidmodemax "1"
seta s_khz "44"
seta ter_error "4"
seta ter_maxlod "6"
seta ter_maxtris "24576"
seta vss_draw "1"
seta vss_maxcount "15"
seta r_uselod "0"

WinterSnowfall: In case anyone stumbles upon this thread in the future, know this: the only line that is actually needed in autoexec.cfg to fix the skybox is:

seta r_forceClampToEdge 1

Vintage1701: Guys I think I found a fix.

I installed reshade 4 and copied the max settings lines into my autexec.cfg file that I had to make - basic instructions on the PCwiki.
However, I did this before and it didn't seem to work so I must have done some extra steps that I didn't do last time.
After doing this, the game had some lag and centre screen tearing which I fixed by forcing vsync in my intel graphic panel (Aswell as adding x2 anti aliasing but not sure if that's needed.
I also increased the r_subdivisions to 3 as suggested in the pcwiki under their max settings but not actually on the lines.

Give this a try and let me know if it helps!

link to the pcwiki page:
[url=https://www.pcgamingwiki.com/wiki/Medal_of_Honor:_Allied_Assault]https://www.pcgamingwiki.com/wiki/Medal_of_Honor:_Allied_Assault[/url]