You can specify value (6 mH) and tolerance (+-10%), but not joint values-and-tolerances. So if you really need at least 6 mH minimum, you technically want to search >6.7 mH +-10% and >6.3 mH +-5%, etc, but that's extra work.
Sometimes the parameter you care about simply isn't available in Digikey's filter, because it's a little obscure like... high-frequency CMRR, or something. So you have to dig into each part datasheet one at a time. That's not really Digikey's fault though; they've tried their best to guess the parameters that are most important, and nobody else has done better.
Where it does get very frustrating is when you need to search through ranges of ranges of values. Like, if your application has a supply voltage that could be between 3.3V and 5V, then you want to filter out parts that require an input voltage higher than 3.3V, or are damaged by an input voltage below 5V. But there's rarely an easy way to do this; often Digikey has one column containing value ranges like "1 - 4V", "1 - 4.1V", "1 - 4.2V"... "1.1 - 4V", "1.1 - 4.1V", and so on. Some of their filters have gotten smarter, but many are still like this, and it takes a long time to go through and select all possible acceptable parts and reject all inadmissible ones. So to save time you end up just guessing at a few likely ranges of values, but then later you discover that there's one really good part that's perfect and cheap but it can tolerate voltages all the way up to 25V for some reason, and you just filtered it out early on because it would have taken too long to scroll that far down.
Searching for connectors can be very frustrating, because there's usually no easy way to look through related parts in a connector family, like to find matching male and female crimp pins and their respective housings.
A lot of frustrations like that are very common, especially when approaching a design from a blank slate.