Why would my clutch work perfectly until I drive over 50 miles then chatter afterwards?

That happens when you change the clutch and not the flywheel. The clutch leaves material on the flywheel and pressure plate when it beds in. If the material is not evenly distributed, you will feel the chatter.

pressure plate could be misaligned

Could be an adjustment issue. However, if you changed the clutch but didn't have the flywheel resurfaced at the time, then tenspeed's answer is likely the cause of your problem.

Depending on the year, it may be an issue with the separator plate. There was a design flaw in the 2005-2007 Mustang separator plate causing the bolts to rub off the plate. Problem was resolved in 2007 with a redesigned pressure plate. Expensive job if you bring it to Ford dealership. Not the case if you know an independent mechanic.

I WOULD ALSO AGREE WITH TENSPEED'S ANSWER. THIS IS WHY YOU DO EVERYTHING WHEN REPLACING THE CLUTCH. FLYSWHEEL GOES TO THE MACHINE SHOP TO BE TURNED. REPLACE:l PILOT BEARING, PRESSURE PLATE, THROWOUT BEARING. CHECK BEARING ON THE FACE OF TRANNY. BEHIND FRONT BEARING RETRAINER. BECAUSE THE ONE THING YOU DON'T DO, WILL BE THE NEXT THING YOU WILL BE DOING. TAKING IT ALL OUT AGAIN!!!!!