The Blue Star seems more popular on some web sites than any place else. They seem to get a lot of press here.
The units I have used by BS have each had some fit & finish issues. Frequently they are missing screws or other details.
Currently I have a client going through a lot of grief with their service.
The fit & finish issues based on the products I have seen from BS is normal.

My BS does not have any fit/finish issues, nor does it have any sharp edges.

The 36" measurement means counterheight. You definitely want the 11/16 above your counterheight otherwise you'll have large gaps once your granite goes in! If you look at the sides, you'll see that the side trim is 11/16" high; that's the part that extends over the counter. Underneath that trim is a slightly wider piece. That wider piece needs to be even with your counter level so the counter can fit up against it tightly.

we installed it the same as alku. Our counters are 36" from the floor, the BS sticks up 11/16" from that.

The interiors are very very sharp! yikes, we had to handle the appliance several times with the grates removed. make sure you wear gloves. We also found that the screws stick out the back, unevenly. Although the rangetop is solidly built, it lacks finesse compared to my other stainless appliance.

Alku05 and Pharaoh,
Thank you much for the info and Alku05 the pics are great! All will be very helpful for my DH.

What did you use underneath your unit to raise it up to the 11/16 above your counter? Or was your base cabinet that it was installed on already the correct height?

I built my cabinet (with the BS at hand) to hold the range top to the correct height.

Here is a photo.

You will find that you can look your unit over and maybe find a screw that could be tightened or a piece pulled in a bit but overall, the unit should be pretty solid. One knock that BS gets over some of its competitors is fit and finish. We had Wolf first and now have Bluestar and did not rate fit and finish as a huge issue but only minor. The difference in delivered performance as wellas burner and grate design was a huge plus in Bluestar's favor.

Also, avail yourself of the Bluestar white glove service if you think your unit needs some cosmetic adjustment as well. As to sharp edges, you will find that to be a problem with Wolf too in those areas not meant to be handled or worked around except for maybe during set up (inside edges, underneath etc). I have no experience with others although I am suspect they are no different. I can tell you that cut myself pretty badly the first time I removed the baffles from my Wolf vent hood. I also got scrapes and nicks when taking the Wolf apart for cleaning in all those out of the way areas. I agree the drip tray edges are more sharp than I remember Wolf being but this is very easily remedied by taking a fine honing stone and running across those sharp edges to deburr them. Should only take a matter of minutes but yes, I would suggest Bluestar make that a part of their finishing process since the drip trays are meant to be handled...again, minor point.

The 36 inch from the floor requirement in the spec's are more of a guideline. Whether it is 35 inches or 37 inches from the floor is less important than the clearances above the final installed surface, particularly the hood but the hood also has a range of clearances from about 30 inches to 36 inches I believe depending on preferences, application, blower sizing and code requirements.

As to getting the correct height above the countertop, use shim strips if the existing depth is not correct. Hopefuly the base is quite level to start with. If you need 5/8 inches to get your 11/16 raised height, cut a 1x2 by the width of the opening from a piece of 5/8 plywood etc. Place a shim strip flush with the front of the cabinet to have a surface to nail the final trim strip to, one in the back and a center strip for good measure. Also, don't obsess over an exact 11/16 final height. If its 5/8 or 3/4 it won't really matter, mine turned out at 5/8 when all was adjusted out and its just fine. This is especially true of you are using a stone or similar type counter surface that is impervious to heat.

Once installed, you might find my comments on the post "cooktop vs range top -- how bad is the gap?" on sealing techniques that work really well once installed.

Bottom line is - Don't worry! Be happy! its not that critical or fine a science and you should spend more time (within reason) enjoying your unit than worring if these measurements are spec'd out to the exact 1/100th of an inch.

Where are you seeing a requirement that the max height from the floor for the rangetop is 36"? Is it this sentence in the installation manual: The unit may be installed directly adjacent to base cabinets at a maximum height of 36""? The sentence structure is ambiguous - "at a maximum height of 36"" could be applied to the range height or the cabinet height. I'm pretty sure they mean the cabinet height.

Also, they don't have a manual for the rangetop (unless something has changed since we got ours) so this is really the range manual. The cabinet height requirement is probably because a higher cabinet would be too high for the adjustable legs of the range. Their documentation is so range focused, that when we opened the box for our range top the first thing we saw was a notice packed on top warning us not to lift the unit by the oven door - kind of pointless when there is no oven!

We hadn't ordered the cabinet under the rangetop quite high enough (our GC didn't figure on the 11/16 above the adjacent base counter when he calculated the height of the under rangetop cabinet as 36" minus the height of the range top. My husband installed a plywood shelf on top of the cabinet to raise it enough (the GC's guys would have done it but my DH wanted to make sure it the support was very sturdy). The GC's guy cut a piece of trim in our cabinet material to go in front of the plywood.

I have the 36" and don't find the drip pan edges to be sharp. I change the foil every few months and haven't had any problem handling it. The only fit and finish issue we had is that the "island trim" has two screws that are above the counter top height - it seems like they could have planned the attachment to have all the screws below the counter to have the trim look smooth. Fortunately our granite fabricator didn't cut the rangetop opening square and made us granite trim for the back and sides to cover the error which also covers the screws.