Well the title is a bit misleading.. lets focus on wood burning items first.
a) the number one item by far is missing fasteners in woodstove pipe connections. Easy to see! If they are missing those what else in home is being overlooked? Perhaps simply lack of knowledge – but where else is that knowledge lacking?
b) the second item is missing firebricks or refractory bricks. If the stove is missing bricks then it is not how it was tested for certifications. It can not be used or should not be used until fixed. An easy fix by the way – I carry bricks and woodstove screws with me at all times.
c) defects in single wall pipe – although no where near as common it is very dangerous. Had a Barrie Home Inspector who missed a single wall pipe in Penetanguishene that was not completely closed – in fact when I tried it would not stay closed and had to be replaced. Yet shown as okay by Home Inspector! Clue when first fire when smoke entered room. Had another one in Orillia by another Barrie Home Inspector where single wall pipe had several rusted pin holes right through to inside, taking pipes outside and holding up to light you could see daylight entering through holes! That same stove was also missing screws at joints and refractory bricks in firebox.
d) system needs cleaning – around 80% of all systems I do an inspection on need cleaning – yet this simple item is often missed by Home Inspectors.
e) improper chimney height – many Home Inspectors are not able to accurately determine chimney height from the ground it seems.. and many fail to go on to the roof!
f) defects in chimney, chimney crown or flashing. Another one you really often need to be on roof, up close and personal to see properly any defects.
g) improper identification of heat form versus insert. This is very common it seems – but not as high on the list as heat forms are not as common as inserts, woodstoves, etc.
There are likely others. Bottom line a Level 2 Inspection is necessary on any property sale/transfer as per NFPA 211. Protect yourself and if the Inspector can not do a Level 2 inspection then find somebody who can.