I have to disagree with the concerns folks are expressing about solid wood planks used for sheeting. Any house built before the 1970’s most likely has a conventionally framed roof (rafters- as opposed to trusses), and solid wood planking for sheeting. Some people seem to be envisioning what is called skip sheeting used for wood shingles in various areas. Skip sheeting is very rare and practically unheard of now-a-days. The gaps are not fractions of an inch, but several inches, about five or five and a half the few times I installed it. Composite or fiberglass shingles placed on skip sheeting would not last one season (also skip sheeting provides almost no moment or sheer strength).
Properly installed plank sheathing is almost as good as plywood and better than OSB in my opinion. It does not have the sheer strength of sheet goods, but as long as the wood itself is not rotten or so brittle it cracks every time a nail is driven into it, and it is properly nailed to the structural elements (rafter or truss), it is a fine surface for shingles. Three quarters of an inch is quite a bit of shrinkage, but there needs to be some gap between the boards so during humid times there is room for the planks to expand. The usual spacing is the diameter of a 16d nail, but if the wood was wet when installed that (approximate) 3/16th of an inch may have grown. About a half an inch is the most I have seen, and back when solid wood sheeting was common most construction lumber was kiln dried. It also seems unlikely to me that the planks had different thicknesses. Lumber yards have been producing S4S boards since forever; even if codes allowed it, the cost savings of using rough-sawn, wet lumber wouldn’t be worth it. On the other hand, unless the roof was designed for moment strength (sheer panel) the planks would not need to be structural grade or kiln dried. (Also you folks back east use a different building code than the UBC we use out west.)
In any case, a shingle can support itself across an occasional ¾” gap, and if the installers had any professionalism at all they would know if a nail missed entirely and drive another one to replace the shiner (can be seen from the underside because it is not in wood- it literally shines). In fact they should pull any shiner too. Even if they were using pneumatics and couldn’t tell from resistance if they hit or not, they almost certainly were using wide crown staples so even if one leg missed the other likely hit the plank.
Now I think spending thousands of dollars on home repairs and not even being there when they start and when they finish is foolhardy (especially if you had trouble with this very same work recently- personally I would have been there to be very sure I was getting what I was paying for). Still, there is no need to worry because they didn’t sheet over the planks. As long as they stripped all previous layers of shingles everything should be fine. That being said, I do have some concerns however. You are mentioning tabs sticking up or not laying flat. Does this roof have any round elements, or rolling pitches? What I am asking is, are all surfaces a flat plain? Because if there are tabs not lying flat that may indicate the shingles were not shipped or stored or installed properly. Shingles are bundled together and shipped flat on pallets for a reason. If random tabs are not laying flat on a flat surface…… why is that? Have they been riding around in the back of some truck all catawampus for a couple of weeks (or months)? Were they thrown up onto the roof and landed in a twisted position- then left that way for hours or days? Or most likely, were they installed in a buckled condition and do they have torque within them that will diminish their lifespan? (Picture the straight line at the top of the shingle being nailed so it has a slight ‘V’ to it- they put the first two staples/nails in while it was running very slightly down hill, then pulled the loose corner up to the correct height. This is a very typical rookie mistake. It will make the center tab want to lift up off the surface. And yes some warm days cause the weight of the tab to overcome the torque that is making it float above the surface. But that constant torque will cause the shingle to rip over time—a much shorter time than it should [i.e.: the warrantee period]. If you have several places with this condition, and potentially more were the error was not enough to make them float, that could shorten the lifespan of your roof. It may be possible for someone like a home inspector service to write a report that states the shingles were not installed properly (if they were in fact improperly installed).
Your folks shouldn’t have paid the balance when threatened, when a contractor knows they have liability they often bluff to avoid having to explain their actions to the registrar or someone else who knows the tricks and can spot their bullshit. In this case it sounds like they talked the folks into an overlay they didn’t need, put the cost into the price but left it out of the contract, and once your folks signed it – cancelled the sheeting and pocketed the cash. The supervisor might have even been sent out of town because he spoke up for your parents. (I can picture this exchange:
Supervisor: “I sold them the upgrade; we make the profit, let’s just give them what I promised them.”
Owner: “They signed the contract without the plywood in it, they are okay paying that price.”
Supervisor: “They are okay paying that because they think they are getting plywood underlayment.”
Owner: “They should have read it before they signed it, buyer beware.”
Supervisor: “But it is just …….”
Owner: “Don’t worry about this. I will take care of it, but I need you to go to Michigan tomorrow …”)
It might be worth paying for an inspection, or at least contacting a company to see if it is an option and how much it might cost. Are your parents okay with the price if the roof lasts for twenty or thirty years? If so, then don’t fret the three quarter inch gaps in the planks; it is unlikely more than a few nails hit nothing. The lack of plywood or OSB is not a critical factor; there are a hundred things more important. How steep is this roof (what is the pitch)? Does it have Yankee Gutters? Do you get lake effect snow? Does the accumulated snow on your roof freeze and thaw every day (expand- contract, repeat day after day)? Did the installers do a proper job? How long does ice/snow/water stay on your roof after a storm? Do you get strong sustained winds or very strong gusts of wind often? How often? How strong?