[SalesForce] VisualForce page with custom controller and lookup causing JavaScript UI issues

I noticed that I'm experiencing UI issues with every Salesforce instance that I have access to when I create a custom VisualForce page using a custom controller and that I display a lookup field on it. This is happening on every browsers that I tried (IE7/8/9, Chrome…).

Here's an example with a custom controller:

This example VF page is using a custom controller called MyCustomController:

<apex:page controller="MyCustomController">
    <apex:form>
        <apex:inputField value="{!c.AccountId}"/>
    </apex:form>
</apex:page>

Here's the controller (I coded this on-the-fly in the browser, didn't test it (just for the example)):

public with sharing class MyCustomController {
    public  Contact c   { get;set; }

    public MyCustomController() { 
        c = new Contact(); 
    }
}

Then, when I head to the page with the lookup field and I try (for example) to toggle the sidebar, there's nothing happening when I click on it:

Also, the tab do not seem to stack anymore when it's larger than the screen width, generating an horizontal scrollbar:

Other UI issues also occur, but they are a little bit harder to explain/show. They all seem to be JavaScript-related.

This is only happening when there's a lookup field displayed on the page. When I add any other fields (number, text, etc.), this isn't happening. When I extend a standardController, I do have the same issue.

Here's an example with a standard controller:

<apex:page standardController="Contact">
    <apex:form>
        <apex:inputText value="{!Contact.AccountId}"/>
    </apex:form>
</apex:page>

Using the standard controller, I can now toggle the sidebar and the tabs are stacking correctly, without horizontal scrollbar.

When I look at the Chrome Developer Console, I get this error using the custom controller:

Uncaught TypeError: Cannot set property 'onkeyup' of null 

Using the standard controller, I get this message (not an error):

Resource interpreted as Script but transferred with MIME type text/html: "https://na5.salesforce.com/servlet/servlet.Integration?lid=#######".

Any idea how to fix that? Thanks a lot!