Does Airbus have a production problem?
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.