Possible workaround - performed adjustments, works everytime, limited to no stick.
I've been dealing with the same stuck issue for a while too. Here's what I've done to get passed stuck issues.
1 - Create an exclusion in Antivirus for the game folder, "SplinterCell.exe" file and the save game locations and files too.
2 - Set "SplinterCell.exe" to run as administrator. Right click on the exe, properties, Compatibility, Run as administrator. If this game is run for all users try setting to run as administrator for all users.
3 - In game settings change the default jump and action keys to bypass sticky key feature. So you can jump rapidly. So make the space bar jump and the shift key action.
I've had limited to no sticking. If there is sticking than the jumping as suggested by others works just as well... and even better when jumping is not mapped to sticky key.
I'm playing the PC version as bought from Steam. I'm onto the Oil Rig level in Splinter Cell, and find that if I climb up the ladder, I'm then stuck in position on the platform above. In the following walkthrough video, at 0'16", it shows that you should be able to walk off this platform along some pipes. However, in my case, once I try to move onto those pipes, Sam cannot move (only rotate). Anyone else seen this problem?
Yeah, I also got stuck every time I tried to sneak past that point. I noticed that moving at max speed (I was crouching) helped with that. Fisher just kind of bumped over the point he normally gets stuck at.
And at the zipline just after that, you have to manually let go before Sam lets go automatically by himself. Instead of trying to grab the ledge of the platform (and failing to do so every time), he grabs on to a beam to his right.
If you're still having problems, don't go up the ladder! As you begin the mission there is a pipe directly ahead. Its rooted in the sea. This can be climbed. You will need to change your position on the pipe near the top to reach your jump off point. This will leave you on the correct side of the barbed wire to continue.