This example may seem perverse. After all, surely any reasonable person would move around some money in this situation and spend more on gas. But the thing is that lesser mistakes just like this are occurring every day with this system.
Example: You go to the store and milk is more expensive than usual (something about the sequester?) Because you have your limited grocery envelope, you have to respond to this by buying less of some grocery. You could buy less milk, or fewer veggies, or less pasta. However: It may very well be that you'd rather keep with your normal grocery purchase and cut back somewhere else — say, two fewer lattes this week. But because the "coffee" budget is separate from the grocery budget, you end up with the same number of lattes and fewer bananas.
Add up a lot of examples like this, and in the end what you buy may look very different from what you would buy if you thought about all of your dollars as interchangeable.
And the separate envelope mistake can really cost you. Usually, people have an envelope for savings — some amount you'll commit to putting aside every month. Now imagine you overspend for Christmas and end up with $2,000 in credit card debt. You'll plan to pay it down using the money in your monthly "gift" envelopes since, after all, you spent it on gifts. And now you're carrying around credit card debt while still adding to your savings every month.
This is a huge mistake. Unless you are a much better investor than most of us, you're probably collecting only a few percent interest on your savings account. And your credit card is likely charging in excess of 15 percent interest. The difference between paying down your credit card bill and adding to your savings could be hundreds of dollars over the year.