on most airliners, there is no beeping when you cross a waypoint in the FMS. that would get real annoying when the waypoints are under a minute apart (departures and approaches) and i'm trying to concentrate on hand-flying the plane.
almost all airliners designed in the last 30 years are centered on the "Dark & Quiet" flight deck concept. if everything is normal, and all systems are as they should be, then there will be no lights on over/inside switches & buttons, and there will be no noises. this way, when something does go wrong, we know about it immediately. if we get a caution message, there's a "ding" and the master caution light that's right in front of my face blinks amber at me till i cancel it. then i look to see what the message was, and run the appropriate checklist.
in my airplane, if we pass the last waypoint in the FMS, we will get the "ding" and caution light, as the computer has no where else to go, so drops out of LNAV mode into ROLL mode. all roll mode does is, ironically, keep the wings level and on the selected altitude.
its really easy to see why they went 100 miles past the airport, as they were made away about 5 minutes before passing the field. it'll take about 15 minutes to figure out what the proper frequency is for the altitude and location you're at, then establish communications with the controller, and get re-sequenced back into the arrival streams. and at the standard cruise speed of ~500kts, you cover a mile every 8 seconds or so.