Granted that the 1953 version of "Titanic" (Clifton Webb/Barbara Stanwick/Robert Wagner/Audrey Dalton) did not have the special effects and later historic information of the 1997 version (Leonardo di Caprio/Kate Winslet).
However, some goofs in Titanic shown striking iceberg on wrong side, shadow of Titanic on iceberg, ship sinking in one piece, etc. Also note that the same scenes were used in a short sequence of "The Unsinkable Molly Brown."
Actually I dont think you can call the ship sinking all in one piece as a goof in the movie as of the time of filming the commonly accepted way the ship sank was all in one piece.
Hey, another one I saw as a kid (see the A Night to Remember board), and I just saw the last 20 minutes or so on tv a few weeks ago.
Wow, what a stoic way absolutely everyone left on board behaved in this film! I realize that may have been the movie style back when this film was made, but it's a little hard to swallow.
Not really a nit, but this movie just ends. The Titanic goes down, and that's pretty much it!
When the Cameron crud was on TV, I told my wife... "I know how it ends. The ship sinks." he he
Wow, how prescient of you! That's amazing!
Was Mrs. ScottN mad at you for blowing the end of the movie for her? 
Cameron's film had the advantage of dazzling state-of-the-art CGI visual FX,but after the documentary-style "A Night to Remember,"I much prefer this Titanic film.I enjoyed the actors & story much better,& the movie moved right along.
I saw this version a few years back. It didn't have the same drama as the modern versions do.
Also note that the same scenes were used in a short sequence of "The Unsinkable Molly Brown."
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Those same sequences (IIRC) were also used in the pilot of The Time Tunnel. Talk about recycling. 
Wasn't this called A Night To Remember?
No. This film was an American production. A Night To Remember, a British production based on a book by Walter Lord, was released in 1958.
How many Titanic movies did they make?
From Wikipedia, here's a listing of movies, miniseries and series episodes concerning the Titanic.
That's a lot!
People really like watching ships sink. ;-)
So it seems.