The calendar on the HTC One mini has five different types of view: Month, Week, Day, Agenda and Invites. You can swipe between different months/weeks/days like you would through tabs in other Sense 5 apps.
Adding a new event is quite straightforward and you can also set an alarm to serve as a reminder. Naturally, the Calendar supports multiple online calendars (including Facebook), only one of which you can sync with your computer. You can also easily show/hide the ones you don't want.
The Agenda view shows a list of all the calendar entries from the recent past to the near future. Invites view only lists events with invitation info attached to them. The day view also shows the weather forecast at the top of the screen, which is a nice touch.
There is also a calculator on board. It is nicely touch optimized with big, easy to hit buttons. Flipping it horizontally enables some more advanced functions like logarithms.
The Clock app comes with World Clock, Alarms, Stopwatch and a Timer. The World clock is like a mini Google Earth - it shows a 3D globe and you can rotate and zoom in on it freely. You can add cities that are pinned to the globe (and also visible as a list below it).
The alarm clock application can handle multiple alarms, each with its own start and repeat time. The stopwatch and timer are pretty self explanatory.
The HTC Tasks app is here as well. It does exactly what the name suggests and can access your Google Tasks. There is no location-based reminder support unlike with Any.DO, iOS's Reminders, etc.
HTC Note app is also onboard. It is somewhat similar to Samsung's SPen - you can take various notes, add drawings, pictures and dictations. Sharing and printing options are also available.
HTC's Weather app is here too. It became popular years ago with its cool weather animations and widget. You can preset many cities across the globe and it uses the AccuWeather info (much like Samsung and Apple do).
The Google Play Store features several scrollable tabs - categories, featured, top paid, top free, top grossing, top new paid, top new free and trending. Apps usually have several screenshots (some even offer a demo video) so you can get an idea of what the app looks like before installing it.
You can also check out comments and ratings, as well as the number of downloads and so on, to help you decide if the app is worth it.
The Google Play Store is full of all sorts of apps, but in some countries it also offers music, movies and TV shows, books and magazines.
The HTC One mini has a built-in GPS receiver, which managed to get a lock in under a minute. If all you need is a rough idea of where you are (within 150 meters) you can use the Cell-ID and Wi-Fi network lock, which is very fast as well.
Google recently revamped the UI, but the basics are the same. Maps offers voice-guided navigation in certain countries and falls back to a list of instructions elsewhere. You can also plan routes for bicycles and public transport. A nice addition in the latest version is that Maps shows you a couple of alternative routes like the desktop version of Google Maps.
For navigation, the map will cache the data it needs and will reroute you offline (so you don't need a data connection along the way). The Navigation app itself had its UI polished to match the rest of Maps.
You can also search for nearby POI and go into the always cool Street View.
Popular places around the world feature pictures and reviews by people. Street view isn't available everywhere, but it is growing in coverage and is the coolest thing we've seen on a Maps app to date (that includes Aerial view in iOS).
You can save maps for offline view, which caches them on your device's storage, but keep in mind that not all map info is saved (meaning not everything down to street level like businesses, POIs, etc.).