Why is tape being applied to this jet engine?
It's not duct tape. It's speed tape.


  Speed tape is an aluminum pressure-sensitive tape used to do minor repairs on aircraft and racing cars. It is used as a temporary repair material until a more permanent repair can be carried out.


Probably just got a bit of a gap around the cowling or perhaps a loose fastener or two. It's common practice for sealing minor gaps and things until it's next in the hangar for work.

Whilst I was Googling for speed tape, I also found these:

http://www.askthepilot.com/duct-tape/

This is how the wonderful British "tabloid" press deal with aviation stories.  Top marks for getting the "shocked passenger" phrase in.