As with most of the older Point and Shoots, shutter lag is a big issue with the 5060. I guess that since you have been using the even older 3030, you probably know, and may have come up with your own ways to deal with it.
I had two other problems with the 5060 over a span of about 5 years of using it. I used the indigenous Olympus housing (PT-020) and had the bulkhead break during a dive. Never understood how, but needless to say, the camera was totaled.
At least two other friends who had the 5060 and I had this problem - one that Olympus never acknowledged as a design flaw. We were all using the PT-020 housing. It seemed that at depth, there was enough pressure exerted on the mode dial by th ehousing's knob to cause the camera to do weird things. The symptoms were varied but it all translated into not being able to use the camera and having to send it back to Olympus for repair. I had this happen at least twice (two different 5060s).
As for the pros, I'd say that the fact that I did use it for 5 years before moving to a DSLR speaks for its ease of use and decent performance. I still use it occasionally for land and people pix.