What's the error-correcting capacity (randomly errors, or burst errors) of polar code?
I am not an expert but I think you may be asking the wrong question. Polar codes don't have a meaningful "error correction capability" obtainable as in algebraic codes by (d-1)/2. Alternatively, this is not the meaningful parameter of significance.

For finite lengths their performance is usually analyzed in BEC (Binary Erasure Channel) and AWGN channels (Additive White Gaussian Noise). The well-cited paper On Finite-Length Performance of Polar Codes: Stopping Sets, Error Floor, and Concatenated Design by A. Eslami and H. Pishro-Niki on arxiv here as well as some more recent papers confirm this.