Sure. Here are a few examples. They're all based on my experience with the MongoDB API for CosmosDb. Your mileage with other APIs may vary.

1. CosmosDB has a hardcoded 60-second timeout for queries. That means that queries that take longer than that are literally impossible to run without breaking the query into smaller chunks. This is worse than it sounds because CosmosDB doesn't have some of the basic optimizations that exist in other databases. For example, finding all distinct values of an indexed field required a full scan which wasn't doable in 60 seconds. Another example is deleting all documents with a specific value in an indexed field - again, not doable in 60 seconds. When deleting or updating multiple documents, we'd write short snippets of code that queried for the ids of all documents that need to be updated, and then updated or deleted them by id one by one.

2. Scaling up and down again can cause irrevocable performance changes since there's a direct link between the number of provisioned RUs and the number of "Physical Partitions" created by the database. A new "physical partition" is created for every 10K RUs or 50GB of data. CosmosDB knows how to create new physical partitions when scaling up, but doesn't know how to merge them when scaling down.

Say you have 10 logical partitions on 5 physical partitions, and you are paying for 50K RUs. Each physical partition holds exactly 2 logical partitions and is allocated 10K RUs. Now you had to temporarily scale up the database for some reason to 100K RUs, so you have 10 physical partitions with one logical partition on each one. When you scale back to 50K RUs, you'll still have 10 logical partitions, each with 5K. So now each of your logical partitions has exactly 5K RUs, while before it had 10K RUs shared with a different logical partition.

3. The allocation of logical partitions to physical partitions is static, hash-based and there's no control over it. This means that having hot logical partitions is a performance problem. Hot logical partitions might end up on the same physical partition and be starved for resources while other physical partitions are over-provisioned. Of course, you can allocate data to partitions completely randomly and hope for the best, but there's a performance penalty for querying multiple logical partitions. Plus, updates/deletes are limited to a single logical partition, so you'll be losing the ability to batch update/delete related documents.

4. Index construction is asynchronous and very slow because it uses some pool of "free" RUs that scale off the RUs allocated to your collection. It used to take us over 12 hours to build simple indexes on a ~30GB collection. Also, if you issue multiple index modification commands they will be queued even if they cancel each other out. So issuing a "create index" command, realizing you've made a mistake, then issuing a "drop index" followed by another "create index" is a 24-hour adventure. Over the next 12 hours the original index will be created, then immediately dropped, and created again. To top it off, there's no visibility into which indexes are being used, and the commands for checking the progress of index construction were broken and never worked for us.