Manufacturers provide tables of efficiency loss with different lengths/diameters of refrigerant tubing (it should be in the installation manual left by the installers), but I'm guessing it's not a lot (maybe 2%-4%). Not qute sure what you mean by "installed the air handler backwards" - can you elaborate? Many air handlers are made with a smaller supply opening that the external dimensions - I believe the Carrier is one such model (I'm guessing its an FV4 variable speed air handler?). Again, take a look at the picture in the installation manual or product data document.

I upgraded from a 25 year old mid range Rheem 8 SEER AC with a fixed speed air handler to a new, top of the line Rheem 16 SEER AC with variable speed air handler and saw no difference in electric bills!

Everything has to be done right or there will be little to no savings.

It takes the same amount of Btu/Hr to hold a temp setting whether it is an 8-SEER or 18-SEER; the savings only comes from perfect installation & duct system design.

Doing LoadCalcs & then doing cost-effective retro-work toward downsizing equipment saves on both heating & cooling modes.

Here is a link that might be useful: Air Conditioning System Sizing for Optimal EER & SEER Efficiency

Seems to me with the efficiency improvement of say 20% that you could have gotten away with a four ton. that duct system is really poor, imho. I'd want a tapered fitting on that transition. You want good laminar (smooth) flow in your duct work. That means avoiding places that can cause turbulence and lead to noise and inefficiency.

First off, judging by responses so far, it's going to be difficult sorting good and bad advice. It is with that in mind I reccomend you get Carrier's field rep involved and have him document everything he concludes,good or bad.
Your Questions were;
First question is how much efficiency am I losing because of the 3 concerns listed above.
PLENTY,Too much
Second question is the long term effect on the wear and tear of the unit.
Significant,enough to worry over.
Addressing the pipe alone,7/8ths is 41% undersize or stated another way,7/8ths only flows 59% of what 1&1/8th flows. The additional lingth farthure restricts flow.
If size didn't matter,what possible reason is there to spend more money on larger pipe?????
If seer efficeny rateing doesn't reflect cost of operation,why in the world would anyone invest up to twice the money??
The statment someone above made about requiring the same # of BTUs to heat a given space wherther it comes form an energy hog or energy miser is misleading at best and would be laughable were it not so obsured. The electric KWs required to produce those BTUs is signifinantly different.
You best deffer to somone local you can trust.

"If seer efficeny rateing doesn't reflect cost of operation,why in the world would anyone invest up to twice the money??
The statment someone above made about requiring the same # of BTUs to heat a given space wherther it comes form an energy hog or energy miser is misleading at best and would be laughable were it not so obsured. The electric KWs required to produce those BTUs is signifinantly different.
You best deffer to somone local you can trust."
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The Btu/Hr required to heat or cool the conditioned space of a home or building remains the same regardless of the SEER or AFUE of the equipment; I did NOT say anything about the electrical or energy efficiency of the equipment; except that the only thing that counts is How much of a units Btu/Hr is "Delivered to the conditioned space.

SEER is a small factor compared to all the other factors that can trash "delivered Btu/Hr" & actual efficiency.

Extensive tests were conducted which included new High SEER equipment; the average Btu/Hr delivered was 63% of the mfg'ers Btu/Hr Rating & half the required airflow.

Selling equipment based on so-called SEER savings should not be allowed without "delivered verified testing" with the results left with the HVAC Consumer!

I have worked HVAC since before the mid-1970's & have witnessed those horrendous inefficiencies regardless of the Mfg'ers Ratings...other factors can easily render those mfg'ers Ratings meaningless for the consumer/user. They paid for those Ratings "but never got them due to lack of following 'all' of the necessary steps in order to get those Ratings."

Here is a link that might be useful: Sizing of Residential HVAC Air Conditioning Systems & Ductwork Systems

Which Carrier heat pump was installed? The product data sheet for the Performance Series shows for a 5 ton condenser a vapor line of 7/8 inch diameter shows will have no performance loss up to 50 feet. This should not be a problem. Hopefully he properly flushed the existing line set.

The Carrier installation manual for the FVB4 air handler shows the unit comes from the factory set up for a horizontal left installation. According to the instructions I read it can be converted into a horizontal right installation. The air passes the opposite direction over the coil. It appears this is an appropriate way to do this. A conversion kit is available to do this installation.

The big problem is the plenum. The duct work is chocking the air handler. That duct work should have at the very least been tapered. The existing duct work looks too small for a 5 ton unit. It would have been easy to replace the main duct work and make a smooth transition to the the main branches.

How big are the returns and filters? Most houses don't have the duct work big enough to handle 2000 CFM of air. How big is your house? Did the contractor do a load calculation to determine if your house needs a 5 ton heat pump?

Thank you all for your answers. Here is some additional info.

The unit is Carrier comfort series, model 25HBC. No, the installer did not do any load calculations, if fact, he did not come by the house prior to installation - except an employee came by to work on old unit. He relied on the Rheem installation already in place.

The filter box is 20X30 opening and the old Rheem attic box is slightly smaller than the carrier input.

The house is 2148 sq ft. and 3 rooms are large, 954, 472, 348.

Table 2 in the instruction book for the unit specified a 1 1/8 vapor line with a 7/8 connection.

As far as I can tell, the reverse installation of the evaporator coil may work and deemed OK by the manufacturer, but may not be an ideal installation and I have my doubts about long term effects - cleaning, leaks, efficiency.

I agree, the big problem is the plenum and will have to be replaced. I called Carrier and was promptly told they did not answer those types of questions and to call the installer, which I will do when I get my ducks in a row. I would love to get a Carrier field rep out here, but how?

I believe the installer cut as many corners (at my expense) as he could to put more money in his pocket. I think the vapor line should have been 1 1/8. I think the installer should have known the coil would have to reversed - before he got it into the attic - and should have discussed it with me prior to purchase. I think the Carrier installation team should have re-configured a new plenum instead of forcing the Carrier air handler into the smaller sized Rheem plenum.

What I need is proof.

I have no experience with Carrier field reps. My impression is they get involved if there is an equipment problem that the installer can't resolve. This assumes the contractor has installed the equipment properly.

Are you sure the old Rheem was 5 tons? Regardless of the size, the contractor should have done an inspection of your set up. My initial reaction is the 5 ton unit is too big for your house. The 20x30 filter is too small. You would need two of these filters in order to have adequate air flow. I can imagine the air flow is very noisy which such a small filter and duct work.