I wouldn't be too concerned about the clause you cite above as it refers to civil liabilities to third parties, rather than contractual liabilities to your employer.
In UK law there is a concept called "vicarious liabilty" - i.e. that your employer is liable for "torts" (civil wrongs) caused to third parties through acts that you, as an employee, commit in the course of your employment.
However if you go so far beyond the remit of your job that you are acting 'on a frolick of your own', your employer is no longer liable.
Vicarious liability in English law - Wikipedia, the free encyclopedia
"Negligence" is probably a broader term than "wilful neglect" and "gross negligence", but this clause seems to be clarifying that your employer is not liable for harm incurred by third parties where you are acting beyond the concept of vicarious liability, rather than costs incurred by your employer as a result of your failure to do your job properly (such as the example you cite above, of flap retraction too early/late so that damage is caused).
As a general point, it is possible that an employer could sue you for negligence. However, they are unlikely to do this because: a. unless you are very wealthy, you are unlikely have sufficient assets to make it worth their while, and b. there is the risk that any damages awarded against them would be reduced for contributory negligence - e.g. in your example above, is their bad training what caused you to raise the flaps at the wrong point?