Find Intervals with Most Overlaps
Is it really \$O(n\log n)\$?

Inside your main loop, you have this line:

            currPartial.remove(pointMap.get(sortedTimes.get(i)));


which removes a Point object from a linked list.  This takes \$O(n)\$ time, so your whole algorithm takes \$O(n^2)\$ time.

Not only that, but this line which copies the best list so far is also \$O(n)\$ time:

           bestPartial = new LinkedList&lt;Point&gt;(currPartial);


Possible fixes

You could fix the first problem by using a data structure other than a LinkedList.  For example, you could use a HashSet or LinkedHashSet.

You could fix the second problem by not making a copy of the best solution.  Instead, remember the index i of the best solution.  Then when you want to print the best solution, make another pass through the sorted times doing exactly what the first pass did.  This time, however, you stop at the best index and print the contents of currPartial at that index.