How To Improve Quality Of Work?

I am working in  a Testing and Support environment where there are prefixed deadlines and a lot of rework. I have to do a check out of required source files, test them completely ,fix the bugs  and do a check in of the files . But most of my time is gone in testing the sources because every time I test I do get a feeling that most of the defects or issues in the source files have not been covered by me which sometimes happens and due to which I spend most of my time in testing itself and allot a very less time to fixing  due to which I have to skip the deadlines every time . Can you propose what I need to do to improve my quality of work.

Every kind of work requires proper input by talented people in related to that work. If you could mention in that what kind of work are you talking about, I could help you better.
But let me give you some general tips to improve quality of work.
To be motivated and maintaining friendly environment is very much necessary. In case of any conflict, resolve it by talking instead of avoiding it.
Take a look at Tips to stay Motivated at Work.

Be sure to keep in touch with workshops and training courses regarding your Job to continuously update yourself with the advancements in your field.

Proper planning is necessary. It can be on day to day basis, week to week or year to year depending on nature of work. All the possible problems regarding work that might be faced in future should be evaluated and proper solutions to them should be planned.

Visit:
Tips to get Smarter at Work,
Enhance Brain Performance and Capabilities,
Tidbits on Job Performance.