Before using Asana one of my biggest worries was that my team members might miss tasks I assigned.
Some used to-do lists and notepad tools, others used sticky notes, google sheets and docs etc.
But this was very messy as there was never a unified tool that everybody was using.
Since I always loved organizing stuff I personally did not have that many problems with arranging all my tasks and ensuring none are missed, however, it was not really convenient having to work with notepads, sheets, calendars and more.
My biggest worry though was to ensure that all tasks I assigned to team members are being attended to as I knew at least half of those would be flying around somewhere, being delayed, missed or whatever. I usually had to keep a list of those myself also so I could follow up with team members (yeah you guessed it → way more manual work)
A lot of times this has really stressed me out a lot and I was even dreaming about missed tasks and also caught myself quite some times sitting in bed at night thinking about tasks I have to follow up on with my team and typing a quick reminder note or sending an email to myself to not forget about it.
We worked like this for a while and also tested out different tools before we discovered Asana in 2015 and using it since then. Asana has basically saved me from going insane 
as I do not have to worry that much anymore about work falling through the cracks.
Yes sure you still have to rely on team members adding all tasks to Asana, etc but that is.
Here is a list of Asana features I recommend, best practices and tips I would like to share:
Time Management
Often tasks tend to fall through cracks that are more challenging and people push the due date back and back
→ The project manager or coordinator must step in to assist in setting priorities, whenever team members are struggling to do to
It can also be very helpful to work with emojis to highlight prios even further
Task „Idea“ pool - do not assign all of these tasks with due date directly but assign one task that asks to check all tasks in the idea column or board
Motivation / Feedback / Appreciation
If people feel appreciated and motivated they work faster and more efficient
Delegation is key! - Stop doing everything yourself - Don‘t abdicate (you or another coordinator are still task leaders and they would have to monitor and be responsible for their team)
Avoid demotivation if overloaded - Train the team so they can control their task volume - It‘s ok to say no to new tasks
The workload feature from Asana is great for this as well so you can keep a better overview.
5 Whys - when something is missed do the 5 whys test to find out why it was missed and how it can be avoided next time
Goals - Goals provide an important reminder of the big picture. Using goals helps you to structure all of your work to see what is required in order to achieve the goals. It is also important to celebrate wins with your team.
Rules & Workflows - Set up rules using custom fields as well to ensure no step of the process is missed (as sometimes team members might mark a task as complete although something is still missing. I recommend reading through Bastien’s post about rules: The coolest Asana rules 
Workflows are a great way to ensure as much as possible is automated which also helps to ensure nothing is missed.
KPIs help you keep track of the performance of your team members. Setting up KPIs also helps your team members understand the expectations. It is important to keep in mind that KPIs must be appropriately identified, reachable and realistically measurable +clearly communicated, documented and agreed upon.
Asana - show your team all Asana features and train them if needed. The goal is for everybody to pick the features that help them be most efficient.
Notifications - Team members struggling with delivering tasks on time should enable upcoming task due date notifications so they receive regular reminders
Whenever you want to monitor a task the quick access „create a follow-up task“ button in the inbox is very helpful
Anxieties of team members - have open conversations with your team members + teach them how they can manage them with the help of various tools and features
Give the right task to the right person. People perform better with the things they enjoy doing most. That does not mean you should only assign tasks they enjoy doing, because everybody should learn and progress further, however, I advise you to listen to your team and assign tasks accordingly as this will bring you even more results.
Clear task instructions - some tasks fall through the cracks as team members do not have a clear picture of what needs to be done so they tend to push the due date → always ensure clear info is provided and remember there are different learning types
Subtasks / Subgoals: Big tasks - demotivation as everybody needs sense of accomplishment → split task into smaller tasks, subtasks and/or subgoals
Integrations to be able to create tasks from within Gmail, Outlook, Slack, and many more tools. This ensures tasks can be created from various places → the easier it is for the team the fewer things fall through the cracks
Mobile app - you can even create tasks on the go and also via voice recording (iOS) Voice recognition for iOS • Asana Product Guide
Create SOPs: This is very important to ensure work is done properly. The more SOPs you have for all processes the easier it will be for your team and the faster work gets done
& Develop systems: Where should team members add new tasks, what is important when creating a task, what info to add, etc
And last but not least:
No matter how big the task add it to asana immediately. Why? Because even small tasks will be forgotten throughout the day if not recorded anywhere.
So here is my list of recommended features, tips and tricks on how Asana helps me reduce the anxiety of work falling through the cracks.
I am sure there are many more things I have not listed here yet so any comments are welcome 