But not every airline overbooks flights in an effort to keep seats full. JetBlue and Virgin America were the industry leaders in avoiding denied boardings, with rates of 0.01 and 0.07, respectively.
United Airlines' consumer complaint rate was 4.24 complaints per 100,000 passengers. Southwest had the lowest rate, at 0.25. Southwest was among five airlines that lowered complaint rates last year compared to 2011. The others were American Eagle, Delta, JetBlue and US Airways.
Consumer complaints were significantly higher in the peak summer travel months of June, July and August when planes are especially crowded.
"As airplanes get fuller, complaints get higher because people just don't like to be sardines," Mann said.
The complaints are regarded as indicators of a larger problem because many passengers may not realize they can file complaints with the Transportation Department, which regulates airlines.
At the same time that complaints were increasing, airlines were doing a better job of getting passengers to their destinations on time.
The industry average for on-time arrival rates was 81.8 percent of flights, compared with 80 percent in 2011. Hawaiian Airlines had the best on-time performance record, 93.4 percent in 2012. ExpressJet and American Airlines had the worst records with only 76.9 percent of their planes arriving on time last year.
The industry's on-time performance has improved in recent years, partly due to airlines' decision to cut back on the number of flights.
"We've shown over the 20 years of doing this that whenever the system isn't taxed as much — fewer flights, fewer people, less bags — it performs better. It's when it reaches a critical mass that it starts to fracture," Headley said.
Passengers appear to be checking fewer bags since the industry's shift in 2008 to charging for fees for extra bags, and carrying more bags onto planes when permitted, industry analysts said.
The industry's mishandled bag rate peaked in 2007 at 7.01 mishandled bags per 1,000 passengers, and has since been declining. It was 3.07 in 2012, down from 3.35 bags the previous year.
The report's ratings are based on statistics kept by the department for airlines that carry at least 1 percent of the passengers who flew domestically last year.
AP Airlines Writer Joshua Freed contributed to this report from Minneapolis.
Follow Joan Lowy on Twitter: http://www.twitter.com/AP_Joan_Lowy
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.