Whelp, didn't take long to find an error with the new campaign!
In Mission 3, if you take the high road you end up in the upper-right most room, where there are two enemies and a platform you can climb across to skip the first guard. If you do so... you're stuck. There's no prompt to kill the second enemy, and even selecting 'auto' just leaves the game doing nothing.
I had to manually restart the mission to get past this. Whoops!
This is probably because the enemies with guns (whose bullets you have to dodge) are facing to the right - the wrong way - which means you dodge their shot, then run round to their right so you can fight them face on. That only seems to happen in this particular mission.
...missions are pretty good otherwise though.
EDIT: Same thing happened on Mission 4, in the second room. After riding down the zip-line, I tried to climb above the enemy using the logs, and once again the game just wouldn't let me do anything. Had to restart it to progress. Again, I think it was because I was skipping a gun-toting enemy.
I'm actually recognising these level layouts as being reused from other stages, just given a fresh coat of paint and adding these different enemies. I'm not against that, but I think it's adding these enemies into levels that weren't originally designed for them that's causing these issues.