Lack of APIs. Blackboard is catching up, but other competitors are much further along since those competitors started as a web-based company. The other factor holding these back is the different hosting options. All APIs are available for cloud-hosted, but not for managed-hosted or self-hosted.
Lack of defaults. While highly configurable, Blackboard is really intimidating for instructors used to default course structures. You can lock this down, but our users enjoy the customizability - which causes issues providing for both values. Instructors have multiple ways to do tasks - and often there isn't a clear pathway.
Lack of focus on core. Blackboard keeps releasing new products : Analytics (usage), Transact (purchase / card system), Ally (accessibility), Predict (early warning)... while the core experience lags behind. Blackboard is trying to sell the idea that their stuff works well with their stuff... while competitors keep improving the core system and make integrations easier. Personally, I believe Blackboard needs to refocus on the core competencies.
Lack of communication / proactivity. Blackboard relied on an integration with Crocodoc for assignment markup. Crocodoc was purchased and shuttered by Box, who had a general press release a year out. Blackboard worked with Box to replace this functionality - but DID NOT DO A GOOD JOB. Communication on progress was non-existant, it required an unplanned restart, and there was a massive feature loss. We still experience some performance issues, and it's been over a year since the switch.
Lack of migration pathway. There are distinct differences between self-hosted and cloud-hosted. The migration path from self hosted to cloud hosted is just as complex as migrating to another LMS. Blackboard has been really pushing cloud-hosted as a better experience, but many institutions of our size have had extreme difficulty migrating and some have ultimately switched to a competitor and had an easier time migrating. If you are considering going to the cloud, Blackboard SaaS will probably be as big of a change as a competitor.
Poor Branding. Ultra is a ubiquitous term that Blackboard has settled on, but there are too many Ultras. Ultra was originally the branding for SaaS, a technology that was Vaporware for two years and then ultimately came out half-completed. Then they started offering Collaborate Ultra, Ultra Course View and Ultra Experience. I think there is even now an Ultra theme that is available for Learn Original. They need to find another word, because it's extremely confusing for administrators - let alone instructors.