Cut off the old flower stalks and the yellowed leaves. Water it well and plant it. It will rebound. It just got neglected and stressed at the store - box stores are not known for their great plant care :-)

If the whitish, calloused-looking regions aren't squishy but instead almost have a loose-ish feeling, check for root mealies, especially since the damage seems to rise from the ground. If they are squishy and there's no pest activity, it's most likely rot and you must cut above the soft zones to save any of the plant. If there are pests, you will need to treat them immediately, and the plant may make a recovery; however, the cosmetic damage will remain. The final option IMO is sunburn, which would account for the callousing and apparent shriveling IF the affected areas are hard and dry. What is the soil composition like? Didieraceaens like this Alluaudia grow in almost completely inorganic soil in S and SE Madagascar and really can't handle anything much more water retentive than some large grain sand added, or PIG with finer grain... also, do you live in an area with high UV or UV spikes? When I lived in Florida, such UV Warnings were relatively common, and my more sensitive plants or my plants that are slower to acclimate had to be shaded or bake alive! Knowing these and similar things can help us help you :-) also, knowing these things for yourself can help you keep your plants healthy and happy! Just remember that growing plants is a learning experience, and everyone on this website has left a trail of plant corpses in their path as they've learned more about proper care. So keep your chin up :-)

Mealy bugs? Can you see oval critters that move when you touch them? My first thought is to put in the shower and gently blast them off. I don't know if any of the plant masters would agree with me. I hate using chemicals.

Looks like scale as others have said. Also your soil looks totally wrong, it appears to be very dark peaty and water heavy. Needs to be fast draining and doubt this is...?? Gill