@Pecan_nutjob the liquid in glass thermometers was mercury. These days it can be alcohol, other chemicals, or even colored water.
Accuracy of recording a person's temperature is dependent upon the accuracy of the device recording the temperature rather than the general location (mouth, rectum, armpit, etc.) Most devices designed to record human core temperature (mechanical thermometers, digital ones, infrared, etc.) are considered accurate and will, therefore, record accuaratley no matter where they are placed/directed. If the same instrument is used both orally and rectally, there will be little deviation, one reading from the other.
Average human core temperature is approximately 98.6 ° (F) (my healthy core temp is ~97.8°) and can differ from person to person as well as change throughout the day due to enivrontmental factors such as: just drank hot coffee, been sitting in 56° room for 6 hours, is genuinely ill, and other conditions. The correct core temperature is a range, not a single precise number. I think most ER medical personel would take corrective action for a dangerous level if the reading was 102.8° rather than wait for 103°.
My last visit to an ER was about 7 years ago and my temperature was 'taken' with an infrared thermometer pointed at my forehead.
98.6° is normal, but does not reach the "high" setpoint until it exceedes 100° and doesn't reach "dangerous" until it exceeds 103°. Because it is a range, gross accuracy is all that is really needed.
There is little/no reason to be concerned about accuracy of the reading unless one has a fetish for the math involved over an extended period of time. An experienced back-of-the-hand on a forehead can provide enough information whether an individual's temperature is normal, high/low, or dangerous.
Last comment: I've looked at a lot of 'net articles that claim rectal temp is the most accurate, but none of them are what I'd consider medically trustworthy, and none of them have provided information on scientific peer-reviewed studies to support their claims.