Joomla debugging and site speed optimization

I have a Joomla based Property Portal and have recently installed an update to a component (EA Improved).
This has caused the Front-end to operate a lot slower than before and the back-end to be almost completely un-usable within one part of the component. I have spoken to the developer of the component and they say I need to check for errors etc. Although I am competent at Joomla enough to have gerneral control I lack the background to read errors etc.
This should be simple for an experienced Joomla Developer. I have copies of the component and modules at hand if that shows as being the problem.
If this project is succesful I would be looking to use the individual's/company's services on a regular basis for continual support and development.
This particular excercise needs a very quick turnaround though as we are unable to use the back-end with its current speeds.