The Bayliner 4588 and it's later model brethren the 4788 and even later the Meridian 490 are very popular Coastal Cruisers.
The layout is very long term cruising friendly for a couple based on it's raised pilothouse design.
As far as issues, there are issues with every boat ever made. The 4588 was built in the 1980's and early 1990's and suffers from age and the materials that were typical in boat building at the time.
Things to look for on ANY boat of this vintage are often related to water penetration of wood cored things like decks, and yes on this boat the arch, and the furniture on the flying bridge to name a few.
Lots of things to look for on any particular boat, but none are issues with the 4588 per se, they are the typical issues one would expect on a 40 year old boat.