Remove the display:none, and use ng-show instead:

<ul class="procedures">
    <li ng-repeat="procedure in procedures | filter:query | orderBy:orderProp">
        <h4><a href="#" ng-click="showDetails = ! showDetails">{{procedure.definition}}</a></h4>
         <div class="procedure-details" ng-show="showDetails">
            <p>Number of patient discharges: {{procedure.discharges}}</p>
            <p>Average amount covered by Medicare: {{procedure.covered}}</p>
            <p>Average total payments: {{procedure.payments}}</p>

Here's the fiddle:

You can also use ng-class to toggle a class:

<div class="procedure-details" ng-class="{ 'hidden': ! showDetails }">

I like this more, since it allows you to do some nice transitions: