There doesn't appear to be anything wrong with the story. However, the marriage of the woman in the article to the husband may be in question. If it is a legal, binding marriage, then when he married the second woman before a divorce decree was entered (whether a divorce was already in process or not, which is not clear), then he is guilty of bigamy (more in a second). If the original marriage is not valid, then he's fine.
This actually happens more often than you think, when people plan weddings before divorces are final...
For those that want to argue definitions: For the most part in the United States, at least with laws following the Model Penal Code, there is a very odd legal distinction between bigamy and polygamy.
Polygamy is is when a person has married more than one spouse (or cohabitates with more than one - spouse does not imply marriage), and the spouses are aware of each other (implying that polygamy is consensual, and is part of a practice). It is also defined as a 3rd degree felony.
Bigamy is defined in the Code as someone entering into a contract of marriage with another while knowing that a previous contract was still valid. Typically the spouses are not aware of each other - if they are, they are also in violation. There is also supposed to be a fairly broad allowance for believing that the previous contract is no longer valid, but most states are more strict. It is also defined as a misdemeanor, although I believe Texas has it as a felony.
Of course, the Model is only a guideline for the states, to help provide some uniformity.