What's most important: Notes are taking during lab work, as observations, data, and ideas generated. Notes are taken such that they can be a record for the next scientist to read the notes (which is most often the later version of you!). Notes are organized in a consistent fashion so anyone can find the notes that you took.
Lab notebooks are the foundation of lab work, research, and discoveries. The greatest ideas are worthless if there is no record of them, or if the records are impossible to find and understand. Laboratory science spans time. Such as short projects that take place in a 3 hour lab, as well as long 30 year projects. However our human memories often have trouble recording details in the moment, and then later accurately remembering these details. Furthermore, human brains are independent of each other! In the modern laboratory and workplace, job changes and short term employment are commonplace, however many important projects span months and years. As such, organized notes and records are a vital part of passing on projects, and joining new ones.
Historically, Lab notebooks were always supposed to be written in ink in bound books. Ideas on this are changing as our world is digitizing. A primary reason for such hard copies was to defend patents and inventions in court cases, but such cases are more complex in modern times, and digital lab notes, emails and other digital records are increasingly accepted as evidence. Furthermore, digital copies of lab notes offer many significant advantage; you can search them for key words, copy them in a matter of seconds, and accurately place data from recording devices in them. Software such as Google Docs even tracks edits though time, and enables a level of collaborate lab work not previously possible.
Modern times are filled with an abundance (over abundance?) of information, and often times very complex information which requires expertise to understand. For this reason some of the most important aspects in modern note keeping are introductions or summaries that help readers understand the content, and a structure which helps keep the data organized.
Title page: Authors name, Authors contact information, Something that tells the reader these are "lab notes".
Table of contents: A list which says each lab, and what pages it is located on. When starting out in bound books please leave 3-4 pages for the table of contents.
Notes: Date on the top, Summary or Introduction about what was done in the lab. All observations taken during lab recorded into the notebook.
Fix them, but keep a record. The modern world has immense "fixing" abilities that have arrived with computers. Consider a mistake in a formula found in a text book; how many students (and professors) will get confused, or preform wrong calculations before the mistake is fixed? And even after it has been fixed, the previous version of the textbook still exist. Students who didn't buy the latest textbook will still be troubled by the incorrect formula. Now consider our digital content; as soon as someone with editing/fixing powers discovers a mistake, a correction can be made and updated. Now everyone who views the formula will see the correct version.
Records are still important here. Seeing a mistake made by another (or even yourself) may help avoid the same mistakes in the future.
A good part of being a good scientist involves a willingness to re-appraise the evidence at each step, and in light of new information and ideas. Always be ready to change your mind; the best ideas of today may be ridiculous in the future.
In written (paper) lab notes, mistakes can be corrected by crossing out the old information; and putting in the new information close by (or putting a comment on where the correct information can be found).
Lastly, please use your best judgement! A mistake in a formula caused by a formatting or typing error, likely does not need a detailed description about the mistake and the correction (or the added confusion that comes with such corrections). Simply presenting the correct formula is better for everyone. A mistake in a formula which resulted from an incorrect mathematical derivation, or mistake in the underlying theory, is a mistake worthy of an explanation. The steps which were corrected and the implications on the resulting formula should be explained to help other readers understand why such changes took place.