Many trains have operated with just two carriages, despite operator ScotRail’s pledge to run longer services to meet demand after the line’s high-profile official opening by the Queen.
Passengers have expressed anger at trains being so full they have been unable to get on.
Other problems include ticket machines not recognising the line’s seven new stations.
Over half the 35-mile, £350 million route is single track and operated largely by ScotRail’s diesel trains, most of which are awaiting refurbishment.
Monitoring by the Campaign for Borders Rail (CBR) showed a “significant proportion” of trains since the opening on Sunday, 6 September had been more than ten minutes late, and some up to 17 minutes late over their one-hour journey.
Members reported passengers standing all the way between Edinburgh and Tweedbank, which is between Galashiels and Melrose.
Delays have increased by the extra time taken for passengers to get on and off crowded trains.
CBR chairman Simon Walton said services had been “less than perfect”. He said: “We did expect ScotRail to honour pledges to lengthen all trains in the early weeks to cope with demand - but that hasn’t been the case, with many running in the very minimum two-car formations and consequent overcrowding on some services.”
Robert Drysdale, an Edinburgh planning consultant who has travelled on the line several times, said: “It was particularly important to get first impressions right, but I suspect there has been a lot of alienation.”
Rail consultant David Spaven, author of “Waverley Route - the battle for the Borders Railway”, said: “There have been too many late trains, compounded by too many being just two coaches long – unforgivably, even during peak hours.
“Astonishingly, there have been no special managerial measures put in place by ScotRail to oversee the critical first few weeks of operation.
“This is the crucial period when passengers new to rail decide whether or not to stick with the train, and too many will now have been put off by their first underwhelming experiences.”
ScotRail said disruption had been caused by factors including a train breaking down, signal problems, high passenger numbers and disruptive travellers.
A spokesman said: “Thousands of people have flocked to use the new line, and despite extra carriages being added to many trains, it has been particularly busy on board some services, as expected. At times this has caused delays while these unusually large numbers of customers board and alight.
“In addition, there has been other disruption at times and we apologise to anyone whose journey has been delayed this week.”
The train operator said it was “working hard” to fix the problem which had prevented passengers buying Borders line tickets from a machine at Waverley Station in Edinburgh.