I'm confused; why aim at 260 and not 240, or even a few ticks lower? Seems like that is where the cluster of signals is located.
Regardless, those directions, either 260 or 240, are just a reference point to start from. Depending on your surroundings, variances are expected. In other words, aim, rescan, observe, shift 5 degrees.....and repeat until you find the sweet spot. It's likely that your TV has a diagnostics screen to show antenna signal strength. Try to find the best overall average signal strengths to help reception in adverse conditions. In other words, Ch A at 90% and Ch B at 50% is typically not as good as 70%/70%.
I'd assume that the compass app is accurate enough to get you started. To determine your direction, you align North to the needle and while being squared up behind the antenna, you should be able to get the direction. Here's a simple guide to reading direction:
http://www.compassdude.com/compass-reading.shtml