As for an amount of purchase... I understand transaction fee problems related to these kind of things. That's why I think that people need to realize that if they want to pay by card - they need to buy something more then just a newspaper. Unfortunately we can't jump over the bank charges.
However... it would be a really good idea to build a system, which would take money from your bank account or a credit card once a month for all the things you bought in that month.
With the card it's just swipe and pin. Done.
Also the minimum is against Visa's merchant agreement. You can report them to visa to get that changed. I was at a pub once that said £10 minimum, but just before I was going to argue he said he would charge it up for £10 and give me the change. Fair enough I suppose.
Other stores though it is frustrating, the thing that frustrates me the most is news agents with a $10 minimum when a newspaper is probably less than $2 and the average magazine comes in under to. I've offered to pay $10 for a $8 magazine before to avoid the hassle just to be told that they won't let me so I have to buy something I don't want to make the $10.
I understand the transaction fee problem, but I think the goodwill you get by allowing pay by card no matter how small the purchase offsets this.