Roger Ebert once wrote about that people should be trying to remake properties that didn't quite work rather than say a shot for shot remake of something that was already successful like Psycho. Lots of movies, books, and TV shows had great ideas that weren't quite executed properly. Why not focus on re-imagining them?

That was the basis of Buffy the Vampire Slayer television show and the BSG re-imagining and look how well they turned out. Two movies based on the same source material can be excluded from this like what is called the Woody Allen-Casino Royale versus the Modern One. Chapters of the Bible have also been adapted several times and each one is not really a remake. Stories can be told over and over again liks Christopher Columbus: The Discovery versus 1492.

What this article is discussing is films remaking films like the remake of Sleuth which both featured Michael Caine where the first film was perfectly fine. Sometimes two films aren't really remakes and only share modest similarities like the Taking of Pelham 123. They are what's termed re-imagining.

What films could use remakes(given that any material can be re-imagined)? What films had good ideas that as Roger Ebert said weren't quite executed properly?

The Color of Money versus the Hustler is an example of a well executed remake. The first film had good ideas about a pool shark but was dreadfully slow and didn't have much of a point. Color of Money took elements of the first film and remade it so it was successful.

Some films are great but have bad endings that could be fixed by a simple remake. One example of this is Fatal Attraction which had a great psychological 2/3rds of movie but in the last 1/3rd degenerated into bunny boiler material. Some films could also be improved by getting more skilled actors and comedies could be improved by getting rid of jokes that fell flat.

The next time you want to remake a movie take a movie that didn't succeed in the Box Office. See if it's a film that has small elements that could be fixed(ending, actors, jokes, etc.) and remake the film improving on those elements.