Customers faced hold-ups of at least 45-minutes at The Mound collection point with only one station for pre-bought tickets open at the weekend.
The pick-up points allow people to swipe their credit card and tickets are printed out. There are 21 such pick-up points in the city.
A Fringe spokesman said it had "never been easier" to order and collect tickets.
The main box office in the High Street, The Mound and Edinburgh University are among the collections points, with a box office now a feature in Glasgow's Queen Street train station.
Many main venues - such as the Assembly Rooms, Summerhall, Underbelly and Pleasance Courtyard - act as pick-up points for tickets for any show for the first time this year.
Tickets cannot be collected at every venue as not all have the space or budget to provide box office facilities. Tickets bought online can also be sent by post.
But a bounce back after last year's Olympic dip may have added to the bottleneck.
The festival released 1.8 million tickets last year, but saw a fall of about 1% compared to 2011.
This week venues are reporting between a 20% and 30% rise in ticket sales on last year, and there is more on offer with theatre shows up from 751 last year to 824.
A spokesman for the Fringe said yesterday: "Customers can buy tickets for Fringe shows by telephone, at our box offices in Edinburgh and Glasgow, online, on our app and through Facebook.
"When customers choose to collect their tickets they can do so from the Fringe box offices or our Ticket Collection Points.
"We have introduced 21 new Fringe Ticket Collection Points at venues throughout the city where you can print your tickets for any show in any venue.
"This year it is easier to collect tickets for Fringe shows than it has ever been before."
Festival traffic eased on The Mound yesterday but performers handing out flyers said the crowds came and went in surges - while queues can be an attraction to acts trying to drum up business.
The total number of shows this year is 2871, performed by 24,107 artists in 273 venues.
It has been estimated the Fringe generates £142 million for Edinburgh and the Scottish economy annually.