Does God Make Mistakes?

No He does not. Sometimes we may not be able to see the reason things happen. 

I believe God knows exactly what He is doing and everything happens only because He allows it. 

The lessons learned from each trial make us stronger and we learn to rely on Him more.

If our lives here on this earth were always perfect without troubles when would we ever call on Him for anything?

Why would there need to be a Heaven? If there wasn't any sickness or pain, sadness or death, life would be perfect and we would never pray to God or trust Him for anything.

So when God allows things in our lives we need to learn to trust that He has a purpose for it all.

He's trying to teach us a lesson. Maybe get our attention. Humility is truly the best teacher.

We cannot do everything on our own. We must be humble for God to use us.

1 Peter 5:6 - "Humble yourselves therefore under the mighty hand of God, that he may
exalt you in due time."
We are not promised an easy life. 
"These things I have spoken unto you, that in me ye might have peace. In the world ye shall have tribulation: but be of good cheer; I have overcome the world." John 16:33

Sometimes God allows things to happen so we will acknowledge Him and his strength in our weakness.

James 4:6 - "But he giveth more grace. Wherefore he saith, God resisteth the proud, but giveth grace unto the humble"