Philipp

<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"> You forgot your viewport tag in the head of the page. Add this to the ProcessWire page.

Include the name of the language when you include the JS file?
<script src="js/<?=$language->title;?>-scripts.js"/></script> Code not tested. This should output something like "en-scripts.js".

The length for the field "pass" is 128. You can change this, by going to Setup->Fields, then click on the Filters and activate "Show Built-In fields". Now you should see the field pass. The length of the field can be changed under "Input".
I agree with you that this limit might be set higher because it makes no sense to limit the password.

The text ist comming from the label "login_submit" of the login button.
I'm not sure how you customized this, so you might either want to remove the label on the template or better, hide it with a custom CSS rule.
EDIT:
This CSS rule should hide the label:
.Inputfield_login_submit label {display:none;}

The "user" is basically just another Page. So you can add a field to the user template and access it from the API.
Create a field for your name, e.g. fullname. Or use an existing one Go to Site > Setup > Templates and then click on "Filter". Enable that system-templates are shown Edit the "user" template and add your fullname field. Save Go to your users profile and enter your name On the front end side, access the field as usual with $user->fullname EDIT:
Output the "fullname" field of the user, that last modified the page: $page->modifiedUser->fullname.

Is your profile_image field a single image field? If not, you can either change this in the admin area by setting the maximum of files for this field to 1. If not, you could access the "first" image with the first() method.
$thumb_contest = $contestant->profile_image->first()->size(50,50); If this doesn't work you might have to check if you have the right pages in the PageArray $contestants.

Running PHP Version 5.3.27, memory limit set to 64M and max_execution to 60 seconds. Trying it with 128MB now.
Looking through the logs, I've found some suspicious entries. Time it little bit off: 
[Thu Jan 16 20:12:50 2014] [error] [client 87.165.***.***] mod_security: Access denied with code 406. Pattern match "cc:" at POST_PAYLOAD [severity "EMERGENCY"] [hostname "redacted.com"] [uri "/processwire/page/edit/?id=22354"] 
If this is the issue, Ryan was right. Thanks. Looking into mod_security now. 
EDIT: Solved! Google spit out some interessting links for "POST_PAYLOAD" and mod_security. I've deactivated the POST filtering for mod_security. Just add this to your .htaccess file:
 
<IfModule mod_security.c> # Should mod_security inspect POST payloads SecFilterScanPOST Off </IfModule> Taken from this site (more info)