Don't start watering the plant even more right now - that will only make things worse. The mushy, dark spots are a classic sign of rot, and that unpleasant smell suggests the roots are already affected. This can happen even with supposedly infrequent watering if the soil doesn't drain well enough or the drainage hole is clogged. Aloe vera really needs dry conditions - way drier than most people think.
First, take a look at the soil: is it wet or mushy? If so, I'd take the plant out, cut off the rotted roots with a clean knife (remove anything black), and repot it in fresh, dry soil with good drainage material (sand, perlite). The pot must have a drainage hole, otherwise water will build up. Even a living room window can be problematic if it's very humid - aloe vera prefers it cool and dry.
After repotting, don't water it at all for at least 1-2 weeks so the cut surfaces on the roots can heal. After that, only water again once the soil is completely dried out several centimeters deep. If the leaves are already very mushy, unfortunately those affected leaves can't be saved - just remove and discard them.