Cracked chimney chase and cap can lead to moisture and pest intrusion.
Getting a good look at the attic is important in revealing any roofing issues including improper flashing, leaking vents/ chimneys, and poor construction practices.
The HVAC system is meant to be more efficient than this.
Properly placed air gaps in the plumbing system are necessary for ideal drainage. This setup is lacking the air gaps.
Always remember to check that your furnace condensation drain tube is clear and terminating in a floor or, (with the help of a pump), a sink drain. Tubes that are clogged will create a back-up of the condensation (water) and spill back into your furnace housing. Water on metal equals rust. If you see water pooling or rust forming inside of your furnace, you may have a tube that is not flowing properly.
Corrosion on piping and shut off valves can lead to leaks.
Something you might not be able to see from the ground could really be bad news.
Missing mortar and grout in brick can lead to water and pest intrusion.
Deteriorating window casing or frame might be a sign of moisture intrusion.