Semicolons most commonly join related sentences together. The most common error I have seen in this regard is the use of another mark of punctuation when the semicolon is actually most appropriate.
Consider the excerpt in the cropped image above. Here we see two instances, one right after the other, in which the semicolon is more appropriate than what the writer selected.
Instance #1: Use of semicolon over the comma
I feel like a broken record whenever I say this, but it bears repeating. Writing and speaking are two different animals. Commas do not indicate pauses in writing like they do in speaking. Thus, the first instance (underlined in red in the cropped image) shows an inappropriate punctuation choice in which the writer has attempted to join two complete sentences with a comma. Commas never join complete sentences. The writer has two options for correcting this error.
Option #1: Use a period to end each complete sentence.
This is the standard option, since shorter sentences tend to communicate more effectively to more people. Using this option, the corrected version would read as follows:
Option #2: Use a semicolon to join two related sentences.
The semicolon connects two ideas while signaling that the second further explains the first. Using a semicolon produces the following:
The same two options exist with the next instance (underlined in blue in the cropped image). Thus, the writer may choose between the following:
I don’t think any metallurgist can argue against that; however, it is not a study guide.
In the example here, declaring that the ASM Metal Handbook is not a study guide further expands the idea that no one would likely disagree that the ASM Metal Handbook is a must-have masterpiece. Thus, use of the semicolon is appropriate here.
Which option is better? It depends on what the writer hopes to achieve. The author appears to want an informal tone. Use of the semicolon tends towards formality since it creates a longer sentence. Shorter sentences lend themselves to informal tone. Although readers here are mostly engineers who have education and experience sufficient to test for professional licensure, shorter sentences still tend to communicate more effectively than longer ones.
Thus, I recommend Option #1. However, the use of the semicolon here is very much correct. And an occasional use of the semicolon will not likely formalize the tone significantly.
Again, it all goes back to what the writer prefers; both options in this instance are appropriate. (Hey, look what I just did!) I have only one caveat. Overuse of the semicolon will introduce more formality and reduce readability. That portion of the audience which struggles to understand the meaning being conveyed will increase. Like most things in life, semicolons are best used in moderation. Writers should use it appropriately when they do use it on occasion.