Now that you have a better sense of the affordances of synchronous and asynchronous teaching, it is important to consider the limitations. The University of Waterloo has developed a Keep Learning resource that provides an interesting overview of the advantages and disadvantages of synchronous and asynchronous teaching.

Advantages and Disadvantages of Synchronous Learning

Synchronous Advantages

Synchronous Disadvantages

Students can ask questions and get answers in real-time, as the session is proceeding.
The instructor can gauge the students understanding in real-time, and adjust the session accordingly.
Students feel an increased sense of the instructor actually “being there” – that is, more social presence and instructor presence.
Instructors can facilitate workshop-style classes and run breakout group activities
Live chats or office hours allow for real-time interaction, like a conversation.

Some students might not be able to participate at the required time due to technical or scheduling problems. Some students might be in different time zones.
AODA (accessibility) requirements may be more difficult to meet - for example, providing captioning for a live presentation.

Advantages and Disadvantages of Asynchronous Learning

Asynchronous Advantages

Asynchronous Disadvantages

Recorded sessions allow students time to digest the session content and/or conduct further research before posing questions in a discussion group. This is better for more deliberate thinkers and also, in some cases, for students whose first language is not English.
Students can access the course content, and interact with the instructor and their peers, whenever it suits their schedule.
Students can re-watch recorded sessions to deepen their learning, or to review content prior to a final exam. Students can likewise review threads in discussion groups long after those discussions have taken place.
More democratic: during a live session, only a small number of students will be able to ask questions; in an online discussion group all students can pose questions or make comments.
Allows students to work around unanticipated challenges such as falling sick for a week, or dealing with a family emergency.

Students might feel less connected to an instructor when they are watching a recorded session.
Students might feel less connected to the course overall when they do not see their classmates.
Students might put off engaging with a recorded session because they can always “do it later.”
Asynchronous learning requires significant task initiation skills since none of the class time is scheduled, only the assessment deadlines.
Asynchronous learning equires a higher level of commitment and independent learning skills.

Source: https://uwaterloo.ca/keep-learning/strategies-remote-teaching/synchronous-vs-asynchronous-online-learning