As a work of art it's a pretty unique solution, but over and above issues with serviceability pointed out by Billy and others, the main flaw in my opinion is the complete lack of EMI shielding.
You would not want to be running that amp anywhwre near a mobile phone, wifi device, computer, tv, etc.
Unless the circuit has been designed to reject interference wideband op-amps tend to amplify it with aplomb.
Often this interfererence is not measurable within the audio band, but it sure makes the op-amps get hot.
Before building a headphone amp, you'd better check that it's suitable for your headphones.
Music headphones range from of around 600Ohms to 8Ohms. Most consumer cans are around 32-64Ohms so a simple op-amp may be sufficient.
You may want to consider something different if your headphones are outside of this range.
If space and power are not an issue, the best universal heaphone amp i've ever used was a 1979 class-A design by John Linsely Hood.
I still use one with an Audio Precision SYS-2232A and a KEMAR for headphone testing.
Here's a link to someone who has published JLH's designs online.
http://sound-au.com/tcaas/jlhphones.htmThere are easy to build kits of this design on eBay for less than £30
Good Luck!
Hywel