Different parts of an animal record can be edited quite easily. The most general way to edit an animal's record is by using "Edit Mode". There is a green "Edit Mode" button on animals' profiles just to the right of the tabs. 

After clicking this button, you'll see that most values on the Profile tab will be underlined. Anything that is underlined can be changed. Simply click on that field and you'll see a pop-up to update the value. The only thing that can't be updated on the Profile tab is the Initial Intake Type, as this is a core part of the animal's record and history.

On the Medical tab and Medical Summary subtab, you can also edit the animal's estimated birthdate, age, weight, and spay/neuter information in the exact same way, via the Edit Mode button.

Here's a short video detailing this: Adjust Animal's Weight in Edit Mode

For the other parts of animals' records (behavioral, memos, and rest of medical), different updates can be edited or deleted individually. Just look for edit/delete buttons on the specific entry.