Tips to find Important Bugs Quickly

We as QA engineers need to find important (Blocker, Critical and Major) bugs quickly in a release testing cycle.
Your smoke test should be able to find most of them shortly after installation (1-2 hours)
Good QA engineers should be able to define SMOKE test cases which capture important bugs.

But how to find important bugs fast. You should be able to smell where system is broken. :-)
Here are few TIPS.

1) Test things that are changed. Fixes and Updates mean fresh RISK.
Most of you know this by experience by now.

2) Test core functions before contributing functions. Test the popular and Critical things that the application does.
Test the functions that makes the product what it is. (e.g. Test ETL/Core before admin)

3) Test capability before reliability. Test whether each function can work at all before deep penetration.
Testing all possibilities should be done later.

4) Test common situations before highly unlikely tests. Use popular data and scenarios of use.
(e.g. Use common files from customer before abnormal files)

5) Test common threats before highly unlikely tests. Test with most likely stress and error situations.
(e.g. Testing 100+ using interacting with an Admin GUI is not a common scenario. Simulating 1000+ users sending topup messages is a common stress scenario.)

6) Test for high impact problems before low impact problems. Test the part of the product that would do a lot of damage in case of failure. Where the RISK his hight more testing should be done.
(e.g. Testing an admin module before Core is not acceptable)

7) Test most wanted areas before areas not requested. You can capture this during knowledge transfer session with pre-sales.

Above list is common to most of the project. You can important bugs sooner
--- If you know more about the product
--- Software and Hardware that interact with the product
--- People who use it
--- People who develop it

I recommend you to think about this and improve on this and explore other ways to find bugs quickly.