First of all : over 40 different projects with iteadstudio , zero problems. Some were 2 layer, some 4, so me were batch orders.
Now, looking at your board : this smells like gerber import problems.
If you look at the pads on the left they have a proper square aperture. The pad with the missing track has a round aperture ( you specified square ). So that is a problem in the gerber data !
The track that is missing seems to be of a specific width not used anywhere else. I may be wrong but it looks wider than the other traces.
As for them needing to put on serial info. Every boardhouse does that. Even the giants that do massproduction. Flip over a pcb on a harddisk and it will tell you the tripod or topsearch logo and batchnumber. No escaping. This is traceability.
As for layout of flex pcb ... Your entire design would be rejected. On flex boards you cannot change dimensions in a step. You need teardrops everywhere. Pad to track or track to track dimension changes need teardrops.
There are also rules for minimum openings in the soldermask. They cant make em smaller than a certain size. Its actually the corners that form a problem. Now that it think of it. That could be the cause of your square openings on those pads being changed to round.... You violate the sharp corner distance rule.
Flex board design is a skill in itself and follows completely different rules than rigid boards.
Now on to the 'itead bashing' : itead does not touch your gerber data. The file goes to the boardhouse they use , those guys slap on the information.
Here is some other bits of i fo : you know how they say : no internal cutouts , no internal milling ? Well i have done at least 5 boards with internal cutouts, oblong holes, non plated oblongs and other 'weird shit' they clearly state they won't do.
Here's the secret : most PCB CAD tools (i won't mention names because that would open another shitstorm... Let's call em tools not even worthy of that name as they are glorified pecil and paper replacements) don't generate the proper gerber constructs or excellon constructs for those jobs. It takes manual intervention to intercept these improper constructions, correct them and hope you have all of them... If you miss one, the customer (who is already a cheapscate) will be yelling at you. As this service is targeted to joe hobbyist (who frequently thinks he is super-layout-man because he can connect two pads together) they impose these restrictions.
They have a business to run. They ar not an education facility nor an intensive care institute for defective layouts.
I always include a mechanical layer that holds the itead order number , sku number , the color of soldermakk and silkscreen. A separate mechanical layer that shows the slots, oblong drill holes (like for those power dc jacks) and other weird shit , with full dimension arrows. My CAM data is split in folders : gerber , ncdrill plated , ncdrill nonplated and ncdrill plated slots. All milling paths are on an individual layer as well in the gerber.
This folder structure gets zipped in afile with the order number and sku number ( so there is no discussion)
I use this approach with all my board vendors. I've never had problems , neither with US Based very high end makers, nor Eurocircuits , Vermeulen Printservice , ACB or any other european pcb maker.
I also have never had problems with itead. I send them exactly the same output using the same workflow i use for anyone else. This proves that their pcb fab is perfectly capable of doing 'real' work.
I've done 6/6 (6 mil track and gap) boards with itead without a single question from their side. Send the files and 9 to 10 days later i had the boards in house (UPS Shipping)