Well, most are very complicated and take a long time to explain, so I'll just do the two easy ones off of the top of my head.
The Prime games are canon and take place in between the events of Metroid 1 and Metroid 2. One problem though. After Samus escapes the planet Zebes (from the first game) she goes straight to SR388 to kill all the Metroids. It's in the manual for Metroid 2, the intro to Super Metroid, and it's manual also. I'm pretty sure that it's on the official Metroid website, too. It's under the plot summary or something. Anyway, how can Samus go directly to SR388 when she is cruising through the galaxy when she picks up a distress signal and goes through the all the events of the Prime series? That's a sloppy loophole that could have easily been avoided. A small one, none the less.
In Corruption, we have been told that the Aurora units (aka Mother Brains) were created and developed by the Galactic Federation as use for organic super computers and security systems. But in several manuals and tons of official sources, the Mother Brain was made by the Chozo on planet Zebes as a security and maintenance system. They were the only ones advanced enough to design it anyway. When the Space Pirates invaded the planet, they corrupted the computer and used it for themselves. So how does the Galactic Federation create it? Especially when it was destroyed on Zebes. Another simple loop hole that could have easily been avoided. It just goes to show the lazyness of Retro Studios when they were making the plot for this series.
Those are to quick ones, but there are some really big ones I do for you, but they'll take forever to type out. I'll try to find you the website where they analyzed all of the plot holes that the Prime series created.