Solution 1:

The syntax is just a little off, try:

<li class="list-group-item"
    ng-repeat="question in newSection.Questions | filter:{ Id: '!-1'}"
    ng-mouseenter="hover = true" ng-mouseleave="hover = false">

    <div href="#" editable-text="question.Text">{{question.Text}}</div>
</li>

See a little JSFiddle: http://jsfiddle.net/U3pVM/3845/

Edit:

Example with variables:

<script> var invalidId = '-1'; </script>
<li class="list-group-item"
    ng-repeat="question in newSection.Questions | filter:{ Id: '!' + invalidId}"
    ng-mouseenter="hover = true" ng-mouseleave="hover = false">

    <div href="#" editable-text="question.Text">{{question.Text}}</div>
</li>

Solution 2:

Although @Michael Rose answer works for this case, i don't think it will if you try to filter not equal some object/variable

In that case you could use:

JS:

filterId = -1

HTML:

<li ng-repeat="question in newSection.Questions | filter: !{ Id: filterId}">
</li>

An even more nested case:

JS:

someQuestion = {
   someObject: {
     Id: 1
   }
}
newSection.Questions = [someQuestion]

HTML

<li ng-repeat="question in newSection.Questions | filter: !{someObject : {Id: -1} }">
</li>