The "DOD wipe" is theoretically useful for magnetic media. There can be residual magnitism at the margins that might theoretically be readable using microscopic techniques. It would have to be a pretty important situation for anybody to go to the expense of trying to read an erased disk. In most cases, a single pass will be sufficient.
Both the multi-pass erase process as well as the potential leaving of residual data is helped-along by normal variations in alignment between the head and media.
The Macbook AIR uses flash memory, which is an entirely different beast. When it's erased - IF it's erased - it's erased. Period.
The article alludes to some small amout of data being left unerased. I imagine this has to do with maintainence of spare space (to work around failed cells) while still leveling, making it impossible to erase everything - unless the internal secure erase actually works as intended.
The article also mentions that the internal secure erase isn't always correctly implemented.
I don't think there's really anything you can do with external software to insure that it's truly erased. Best plan is to read reviews, and see if security specialists have reviewed specific products and given them a gold star.