Ok, here is the current way to do this in JRemote. I may make this a sticky later.
Playlist editing in JRemote
First of all, playlist editing requires MC version 19+. If you have a lesser version, the "Save playlist" option will not be visible.
Creating a playlist
From the "Action" button on the "Now Playing" screen, select "Save playlist".
You may now choose to either replace an existing playlist or add a new one by tapping the "+" icon at the top.
All tracks in the current "Now playing" list will be saved to the new playlist.
Editing a playlist
Tap the "Edit" button and reorder and delete tracks as needed. When you are done, save the playlist as described above.
Adding songs
Make sure the playlist you want to add tracks to is loaded. From the "Action" button on the "Now Playing" screen, select "Load playlist".
Now you can start to browse your files and add tracks to the "Now playing" list. When you are done, you need to save the "Now playing" list as described above. Make sure you replace the playlist that you loaded initially.
Quick tip for quickly adding tracks to current playlist
If you are about to add multiple tracks or albums to the playlist, you should change the "Default tap mode". This is the small "=>" icon visible in any file view. The icon is different depending on your selected mode.
From the popup, select "Add to playlist" or "Add all to playlist". This will now be set as the new global default.
Now, when you tap a file it will just be added to the "Now playing" list, instead of starting to play.
Future additions
The version after the next will allow you to save any track directly to a playlist, without you having to load it first.