If your source footage is not shaky, and the output is shaky you need to select the right project setup for your clips and also choose right preset for export to get a good quality.
For the pixelation, you are talking about, i can see a lot of interlacing(distinguishable horizontal lines) in your youtube video, to remove interlacing you need to select a progressive project preset and a also select a progressive preset for export.
When you select a project preset, on the right side you can see the details, that whether the project preset is interlaced or progressive.
Also in project presets, P stands for progressive and I for interlaced.
More information needed for someone to helphttp://forums.adobe.com/thread/416679
Plus Video-Specific Information http://forums.adobe.com/thread/459220?tstart=0
And, finally, the EXACT type and size of file that is causing you problems
-for pictures, that includes the camera used and the pixel dimensions
Read Bill Hunt on a file type as WRAPPER http://forums.adobe.com/thread/440037?tstart=0
What is a CODEC... a Primer http://forums.adobe.com/thread/546811?tstart=0
What CODEC is INSIDE that file? http://forums.adobe.com/thread/440037?tstart=0
Report back with the codec details of your file, use the programs below
For PC http://www.headbands.com/gspot/ or http://mediainfo.sourceforge.net/en
For Mac http://mediainfo.massanti.com/
Once you know exactly what it is you are editing, report back with that information... and your project setting, and if there is a red line above the video in the timeline, which indicates a mismatch between video and project
As both Johns say, this is likely a mismatch between your source footage and project settings. This stuttering can happen if, for instance, you load an MPEG or DVD file into a project that's set up for DV video.
What type of camcorder is your video coming from? And which setting did you select when you set up your Premiere Elements project?
Grin... sounds like a good movie title "The Mystery of the Two Johns"
(sorry for the tangent...)
Thanks for the suggestions! I got the shakiness fixed and you're probably right about the interlacing. How do I remove the interlacing though? I tried right clicking on the clips > Field options > Always deinterlace but that doesn't seem to have worked. I also went in to Edit > Project Settings but I didn't see any options to change it to progressive. Is there a way I can change the project preset to progressive even though I've already started on the project? Thank you so much for your help! I just bought Premiere Friday so I'm still in the learning process =)