This helped me so I want to keep it right here so it doesn't get lost. Maybe it will help you too? ;)

I kept getting complaints from users that the 'convert' button was not available on leads in the salesforce1 app. I searched high and low for a solution and ended up having to build a quick and dirty solution myself.
The app consists of a flow, action, class and VF page.
It sounds harder than it actually was. I am sure that salesforce will be fixing this soon but I put this quick fix for lead conversion in salesforce1 app together for installation:
https://login.salesforce.com/packaging/installPackage.apexp?p0=04td0000000N0nu
After the install make sure that publisher actions are enabled:
From Setup, click Customize | Chatter | Settings.
Click Edit.
Select Enable Publisher Actions.
Click Save
Go to the mobile and click the plus button on the bottom right for all of the publisher actions:
Then click the wrench icon for 'leadconvert'
The app consists of a flow, action, class and VF page.
It sounds harder than it actually was. I am sure that salesforce will be fixing this soon but I put this quick fix for lead conversion in salesforce1 app together for installation:
https://login.salesforce.com/packaging/installPackage.apexp?p0=04td0000000N0nu
After the install make sure that publisher actions are enabled:
From Setup, click Customize | Chatter | Settings.
Click Edit.
Select Enable Publisher Actions.
Click Save
Go to the mobile and click the plus button on the bottom right for all of the publisher actions:
Then click the wrench icon for 'leadconvert'
A new screen comes up with the company name and finally you click 'next' and the lead is converted