Not a terrible ‘error’ - we know what you mean! But still, it’s important to understand the distinction between in first place and in the first place.
In IELTS Task 1 writing we often find ourselves ranking items as follows:
But what if you’re listing rather than ranking? Let's say, for example, that you're listing supports for an argument. In this case you need in the first place, in the second place, etc.:
In this case in the first place means as the first consideration. It's often used to introduce reasons that should be obvious but may need to be emphasised, as in the above example. Notice that it is unusual to continue in the second place, in the third place, etc. Better to switch to secondly, thirdly, and so on.
To sum up..