There is no limit.
The theoretical limit of recipes, etc, within the app is only constrained by the amount of space which remains on your device, and recipes take up fairly limited amounts of space because they are stored in a database. We thumbnail images and allow 1 image per recipe, so images are generally fairly small as well.
How does the app perform with large collections (over 10,000 recipes)? The app has undergone a series of performance enhancements; we've tested it with up 17,000 recipes, and it performs well at that level. Performance begins to degrade beyond 50,000 recipes, but we're working on that.
On a technical level, the way this is done is to perform searching and loading of recipes in the background (not blocking the UI), and we generally only keep a limited subset of objects in memory.