Our Sitecore 7.2 website runs quite fast, the problem starts when we want to change a lot of items on the backend. Even just opening an item takes 5-6 seconds, and saving the same.
I have events handler for when an item is created or renamed, but no more - I can't fathom why clicking on an item and seeing its details takes so much time. Does the debug mode works for the backend too? How can I start figuring out where the bottleneck is?
To troubleshoot performance issues in Sitecore (including the content editor) your best bet is to start with the CMS Performance Tuning Guide. There's a companion to it, the CMS Diagnostics Guide.
Depending on what you find, you may need to read up on indexing, caching, browser configuration - again, lots of the information is on SDN.
For the content editor, for instance, there are some application settings that can make a huge difference to loading items - e.g. Prefetch collapsed sections, show fields from standard templates, which warnings you show in the gutter.
The Sitecore Log Analyzer will almost certainly be very useful to you, if you add some performance counters to the log (though these can themselves impact performance).
You can also monitor caches at the admin/cache.aspx - if your cache deltas go haywire or cache sizes reach maximums then you'll have a performance hit
But I'd start by simply monitoring your server resources while you perform one of your troublesome item updates - that should at least let you know if your bottleneck is memory, CPU, SQL connectivity etc.