Are 低い and 短い interchangable or do they have specific uses?
低い hikui is "short in height" or "low", 短い mijikai is "short in length".
- 私は背が低い - I'm short (in stature)
- 天井の低い部屋 - a room with low ceiling
- 短いスカート - a short skirt
- 髪を短く切る - cutting one's hair short
(Examples from プログレッシブ英和・和英中辞典)
A short piece of string cannot be 低い and calling a low bridge 短い would mean the wrong thing.
I'm putting this as an additional answer because I think it's valid and would have probably remained relatively unseen as a "buried" comment above.
短い means "short in length": length of your hair (髪の毛が短い), time it takes to do something (テストの時間は短かった), or a short distance (スーパーまでの短い距離)
低い means "low". The confusion comes in when it means "short height" (背が低い). However, if you think of being short as having a "low stature (?)" or "(short because your head is) low to the ground", it makes sense.
Also, since you can describe other things besides height with 低い, it's better to remember it as "low": low volume （音量が低い）, low temperature (気温が低い）, low blood pressure （低い血圧）, etc. We can see that when describing these types of things, the definition "short in height" does not make sense.
In English, we would say a person is tall, or a string is long. Though possible in odd circumstances, we would not say a person is long nor a string is tall. With 'short', we put the two categories together. Both strings and people can be short, not in Japanese though.
hikui = opposite of tall
mijikai = opposite of long