What do you like best?
There is a lot of obvious research that was put into making the language, which makes it a very good choice to use in small scale projects that don't require the corporate/advanced features that regular SQL has to offer. This software is also available for many different platforms, which is great for small-time developers that want to use professional database software like this for free. It is also extremely fast, as I've never personally had issues with the speed of retrieving data regardless of the platform I am using.
What do you dislike?
A lot of people dislike the SQL language in general, and often specifically the difficulty to create one-to-many relationships in SQLite, or just the difficulty of the SQL language in general. There also isn't any default encryption, which is a huge flaw for any product that is going to be used publicly and commercially. SQLite is also a single-user system. So, if it is a requirement that your company using a collection of accounts to manage the database, this could become an issue very quickly.
Recommendations to others considering the product
SQLite is a great option for those that are looking for an entry-level database management system that doesn't require any commercial licensing. However, be aware that some issues might arise in the later stages of product development, especially if you are looking to release a product like this publicly.
What business problems are you solving with the product? What benefits have you realized?
IT is really nice to be able to use a platform like this free-of-charge. I suppose this solves the problem of having to finance database software or possibly receive licensing for commercial use of some type of database software.