Is zai4 + ... + li3 really a mistake?
在客厅里坐着一位老人.

The 在 is redundant because of the 里, as 客厅里 already says "In the living room..." and adding the 在 would be saying "in the living room" twice.

So, 在客厅里坐着一位老人 would be saying -- "At the living room in which sits an old man"