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Install the CalenMob Pro app
The iPad mini has a free calendar app but the CalenMob Pro app leaves it in the dust. It has several useful views and is a joy to use. It syncs nicely with Google Calendar and with multiple calendars enabled it is a very useful tool on the iPad mini.
Thanks to @jasonhiner for turning me onto CalenMob.
$6.99 (limited free version available)
Install NOAA Radar HD
The iPad mini screen is perfect for detailed weather tracking and the NOAA Radar app is great. It gives near real-time radar images of your immediate area and the big picture too. The app looks great and is extremely useful.
Change the iBooks reading font
The iPad mini lacks the Retina Display of its bigger sibling which can make reading ebooks less enjoyable. That's a shame as the smaller size of the iPad mini is perfect for reading books.
The book reading playing field can be leveled by simply setting the font in iBooks to a cleaner font. Open up the fonts menu at the top right of the screen and test the different fonts to see which appeals to you. I find the Seravek font to look great on the iPad mini and recommend giving it a look.
Hat tip to @treestman for pointing out how nice this font looks in iBooks.
If you use the Kindle app for reading books instead of iBooks check the next tip to make that better.