Better use kana instead of some weird or wrong kanji if you're not certain
In natural languages, the meaning of words are often extended, changed and modified to fit the speakers needs. Just look up some basic verbs in an English dictionary.
When two of these meanings are far enough apart, we can call it two separate words, and it makes sense to use a different spelling for these. For example, 話す and 放す.
However, often it happens that two of these meanings are rather close and related to each other. In English, we would spell it the same way, and it looks like the same word to us. In Japanese, there are kanji in addition to the phonetic-based kana, and different kanji get assigned to these closely related meanings as well.
Note that dictionaries often list them as the same word. Also note that the boundary between just a different spelling and two different words is a grey zone. Further note that using different kanji for different meanings is done with on-reading-compounds related to the kanji's significance, so it would seem perfectly natural to do this for native words as well.
And sometimes it happens that there are multiple spellings for meanings that are virtually identical and hard to separate.
Until recently (~pre-war), kanji had been more common even for spelling particles etc, and there are some alternate spellings for some words hardly used anymore if ever.
My kanji dictionary 新撰漢和辞典・第六版・小学館 has got an appendix of alternative spellings:
As I said, you won't come across many of the above.
For many words, there is a default kanji that can be used in most or all of its senses. And it may be acceptable to spell without any kanji in the first place.
Some alternate spellings are used for the effect in literature etc. For example, I've seen 嗤【わら】う in a novel a few times.
As for your question, no it is not okay to use just any kanji for a certain word just because it has got that reading. If in doubt, check with a dictionary or default to kana.
The Microsoft IME includes some explanations on how to use different kanji for a word that pop up while converting a word.
Personally, I can recommend the dictionary 明鏡国語辞典 published by 大修館書店; it includes clear notes on different spellings, and sometimes even lists the possible kanji for each sense.
Here's an online resource I found: nihonjiten.com