There should be a list of movies you've already seen and movies on your Watchlist that you've checked off should automatically be moved to that list so you know what you've see instead of it being deleted out of the list.
If you rate the film, it's already on a "list" in your account: Your Ratings. Otherwise, it's easy to create a custom list, and easy to move a title from your Watchlist to that list using the desktop imdb.com (I don't use the Android app enough to comment on how easy it is there.)
To create a custom list, this button appears on any list you're viewing, although it's not so colorful on the Watchlist page, but still in the upper right quadrant:
When you're ready to move a title from Watchlist to custom list, hover over the "+" sign that allows you to add to the Watchlist, and see your custom lists:
Click to add it to the custom list, and click the Watchlist "+" to remove it from the Watchlist. Once it's on the custom list, you can add comments if you like by Editing the list.