Does Airbus have a production problem? Looking up numbers for my answer to the A380 production question, it occurs to me that Airbus is facing a real inability to deliver its latest airframes. The A380 is currently sustaining a build pace of 45 aircraft a year with a backlog of about 150 outstanding orders. The A350, Airbus's direct competitor to the 787, has better orders (781 outstanding), but Airbus has been able to deliver only 5 of those, 4 to Qatar Airways and 1 to AerCap. The A340 ended production in 2011, so the 330 (1370 orders, backlog of 356)  350 and 380  are Airbus's only three widebodies in production right now. The 320 and 321 are backlogged badly, though Boeing has a similar backlog for 737 variants so that seems par for the course in the modern aviation industry dominated by LCCs.

Boeing has had fewer orders for its 747-8 but is keeping pace (92 delivered of 123 ordered, averaging 18 airframes a year) and has an embarrassment of riches in 787 orders (1095 ordered, 295 delivered, on pace for about 115 aircraft a year after ramp-up) and healthy business with the older 777 (backlog of 560, in the ballpark of about 80 deliveries a year since 2010). Its 767 frame, a close competitor to the A330, has slightly fewer orders despite being the older plane, but Boeing seems to be keeping pace (less than 100 backlogged in a total of 1161 orders).

I read these numbers and I come to the conclusion that Airbus is in big trouble in the large and very large jet markets it was planning to dominate just ten years ago; Boeing, by most accounts seems to be out-producing them and thus getting the lion's share of a mostly post-jumbo market. Am I reading this right?
A backlog of orders does not indicate a manufacturing problem. Quite opposite, it is good for the business as it adds stability. Airbus outpaced Boeing on every aircraft expect the A350/787 last year. 

Producing all of the backlog in one year is not a good idea, as investments into the production line would be enormous and after a year, utilization of the line would be horrible. If all A380 were to produced this year, what should they do with the production line next year? A chance of another 150 orders per year coming up is unlikely.

A350 production started last year while 787 started in 2011. The ramp-up of production has already happened for the 787, but not for the A350. According to Wikipedia, by 2018 the production has ramped up to 10 per month, which would outpace the 787 at the current capacity.

https://en.wikipedia.org/wiki/Competition_between_Airbus_and_Boeing

https://en.wikipedia.org/wiki/Airbus_A350_XWB#Entry_into_service

In conclusion, I do not think they have a manufacturing problem. Keeping reasonable backlog is good for the business.