There are two major risks, one of which is very difficult to quantify. So let's start with that.
Kerckhoffs' principle states that you have to assume that only a key is secret, not the means of communication. There's you and your friend, lover or co-conspirator and you communicate. The state knows this, and a search of your properties reveals a OTP was used, generated from some magazine. Assume you read a lot so you have many mags, say 10,000 as you have a rather large bookshelf. Guessing the correct one is only equivalent to guessing a ~13 bit key. That's not a lot. Granted you then have to work out which parts of the magazine were used, but you can see that the state is closing in on you. There are other pragmatic issues to quantifying this like eating the magazine afterwards, but still... Compare that to an electro-mechanically generated key of the length of a Twitter message. That's 1280 bits, which is oodles better.
Another risk is that the entropy rate of the key material must >= entropy rate of the plain text. This is the fundamental requirement for a OTP to preserve perfect secrecy. If your magazine is about fishing or football, the entropy rate of the text will be quite low, say just ~2-3 bits/character. An article by Umberto Eco will fare better, but not by much. Your secret message will have to have a correspondingly low entropy rate. So if you were to try and encrypt binary data approaching 8 bits/byte, perfect secrecy is impossible. Your message would be capable of being easily brute forced. You can mitigate this by using randomness extraction on the magazine text to condense the entropy to 8 bits/character. That still leaves my first and main risk though.
This is one of the fallacies about using such key material, and it's perfectly understandable given human senses. You think that finding the exact magazine is so hard it borders on impossible. It's only 13 bits improbable, whilst to us 10,000 magazines seems a lot. Compared to truly random keys, it's no security at all.