Movies purchased from iTunes get choppy and the image stutters and skips

Question

I have at least 11 movies that I have either downloaded directly from iTunes or received through iTunes because they were bundled as a digital copy with a BD.
I have a mid 2009 Macbook Pro with 8 GB of RAM and a 2.53 GHz Intel Core 2 Duo processor. OS 10.9.5.
ANY time I try to watch one of the movies through iTunes, either on my computer screen or an external display, they reach a point where they start pausing and then speeding up or freezing then playing again a few seconds later having skipped some of the frames in-between, causing me to have to rewind them to see the things I missed. And they don't always skip/chop at the same places either. But it does seem to get worse the longer I watch.  The sound plays normally throughout but the images mess up. I am beyond frustrated by this. I just want to be able to watch my movies and the special features without also wanting to throw my whole system out of the window.
I want to be able to watch these movies on my television, and eventually I want to get an AppleTV so I can stream them, but will that just keep messing up too? Because if so then I don't want to waste my money. (Really I would rather be able to stream them using one of the many devices I already own but that's another issue entirely). I'm a film major and this is very dear to me and I just need an answer.
If anyone knows of a fix or at least not a fix but a dejecting truth about my situation I would appreciate the input.

Answer 1

When you have the problem, note the exact time: hour, minute, second.  
These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
The title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
Each message in the log begins with the date and time when it was entered. Scroll back to the time you noted above.
Select the messages entered from then until the end of the episode, or until they start to repeat, whichever comes first.
Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
The log contains a vast amount of information, almost all of it useless for solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
Some private information, such as your name, may appear in the log. Anonymize before posting.