The time machine is perhaps more dangerous than any other technology that manipulates space and time. Not only can unscrupulous people use it to wreak havoc in the past and take advantage of knowledge from the future, but a single misstep could forever alter the course of history.
Trips through time are exercises in causality. Traveling into the past might set in motion a chain of actions culminating in different major historical events. Characters might return to the present to discover that the Roman emperor Caligula used intercontinental ballistic missiles to conquer Europe and the Middle East. Conceivably, history could be altered in a way that prompts the Soviet Union to invade and conquer North America. Perhaps the characters can't even return to their own time because the person who invented the crucial component of the time machine was never born, for some reason. In short, the permutations of cause and effect can be infinitely mind-boggling.
Temporal paradoxes are liable to stall the development of time travel until someone can prove either that (a) actions in the past by people from the present have, in fact, already happened (and that it was those actions that led to the current state of affairs), or (b) actions in the past that affect the present can be detected and averted by sending someone else into the past to prevent those actions from happening.
Another potential side-effect of time travel popularized in literature is the alternate reality. The timestream in which time travel is invented continues to exist. Situations that create significant changes or temporal paradoxes serves as the locus or intersection point where realities diverge.
The time travelers might encounter worlds very similar to or different from their own. This creates a rich diversity of settings where the established "facts" and "rules" are no longer sure. The nefarious villain recently defeated in a different reality might be a trustworthy ally in this one. A temporal adventurer might encounter a dead companion who did not die in this alternate reality. The possible permutations are infinite.
Time machines that do not actually move are at the mercy of topographical changes and other changes in the locations in which they appear. Never mind that one couldn't construct a time machine in New Mexico and use it to visit Jerusalem in the year A.D. 33. Traveling into the past might deposit you in the middle of a rushing river or under thousands of tons of glacial ice. Traveling into the future, you might find that the position occupied by your time machine now resides in the basement of a futuristic skyscraper or in the middle of a radioactive wasteland covered by ice-the result of an extraordinarily heavy and sustained nuclear bombardment.
Modern language is loaded with slang, jargon, and colloquialisms that would mean nothing to people who lived in the 19th century. Their slang, jargon, and colloquialisms, by the same token, would mean nothing to those who lived in the 18th century. Go back another thousand years, and the words you are reading right now would be all but incomprehensible to the average English- speaking person-assuming he or she could read. Your speech would be equally incomprehensible. Go forward a thousand years, and the English of the new millennium will barely resemble the English of this millennium. Without a Speak Language or Read/Write Language skill for the appropriate era, communication could more closely resemble a game of charades.
Those who travel in time age normally within their own localized time. So, while eons may pass in the eye blink it takes to travel through them, the time traveler feels none of the effects of aging. However, this can work against the traveler. If he were to spend twenty years in his own timeframe exploring the centuries, then return to his starting point, he would, in fact, be twenty years older than he was when he left.