Comma - present participle construction

 Avoid comma + -ing construction. Use the indicative mood and finite verbs instead. 

What I am trying to correct is less an error than an infelicity of style. This really is a neat trick for imbuing your sentences with an extra dash of authorial clarity and control. It also forces you to double check on the correspondence between the subject and the verbs, which is always a good thing. 

First, look at the following sentences: all of them are correct.

1. The new law enables private drivers to pick up passengers and charge them fares, allowing ordinary people to work as taxi drivers.
2. With our new-formula  grime-busting spray, you can clean your house top to bottom in just 14 hours, leaving yourself plenty of time for the important things in your life, such as cooking, shopping and even sleeping!
3. With a rising number of migrants on its borders, Europe is adopting weak policies, leaving itself vulnerable to accusations of complacency.
4. Giving up bad habits actually drains your mental resources, rendering you less able to focus your energies on the really important things such as English grammar.
5. The team played defensively throughout the first half, refusing to take any risks.
6. My students looked bewildered, upset and confused, giving the strong impression that they were unaccountably uninterested in sentence structure.
7. Mario stopped typing, deleted his half-finished essay, left the library, the University and the country, swearing never to return.

All I am asking of you is to consider a different, plainer and more direct construction that uses "and" followed by a  finite verb rather than the   comma-present participle solutions that are underlined and colored pink above.

Why? Because a finite (i.e. an "ordinary") verb is immediately clear: it is more concrete and creates a greater sense of balance or "parallelism" in the sentence by echoing the finite verb that is to be found in the first part.

You could therefore profitably rewrite the sentences above as follows:

1. The new law enables private  drivers to pick up passengers and charge them fares,  and allows ordinary people to work as taxi drivers.
2. With our new-formula  grime-busting spray, you can clean your house top to bottom in just 14 hours and leave yourself plenty of time for the important things in your life, such as cooking, shopping and even sleeping!
3. With a rising number of migrants on its borders, Europe is adopting weak policies, and is leaving itself vulnerable to accusations of complacency.
4. Giving up bad habits actually drains your mental resources,  and renders you less able to focus your energies on the really important things such as English grammar.
5. The team played defensively through the first half,  and refused to take any risks.
6. My students looked bewildered, upset and confused, and gave the strong impression that they were unaccountably uninterested in sentence structure.
7. Mario stopped typing, deleted his half-finished essay, left the library, the University and the country, and swore never to return.

Here they are side-by-side; 

The new law enables private drivers to pick up passengers and charge them fares, allowing ordinary people to work as taxi drivers.	The new law enables private  drivers to pick up passengers and charge them fares,  and allows ordinary people to work as taxi drivers.
With our new-formula  grime-busting spray, you can clean your house top to bottom in just 14 hours, leaving yourself plenty of time for the important things in your life, such as cooking, shopping and even sleeping!	With our new-formula  grime-busting spray, you can clean your house top to bottom in just 14 hours and leave yourself plenty of time for the important things in your life, such as cooking, shopping and even sleeping!
With a rising number of migrants on its borders, Europe is adopting weak policies, leaving itself vulnerable to accusations of complacency.	With a rising number of migrants on its borders, Europe is adopting weak policies, and is leaving itself vulnerable to accusations of complacency.
Giving up bad habits actually drains your mental resources, rendering you less able to focus your energies on the really important things such as English grammar.	Giving up bad habits actually drains your mental resources,  and renders you less able to focus your energies on the really important things such as English grammar.
The team played defensively throughout the first half, refusing to take any risks.	The team played defensively through the first half,  and refused to take any risks.
My students looked bewildered, upset and confused, giving the strong impression that they were unaccountably uninterested in sentence structure.	My students looked bewildered, upset and confused, and gave the strong impression that they were unaccountably uninterested in sentence structure.
Mario stopped typing, deleted his half-finished essay, left the library, the University and the country, swearing never to return.	Mario stopped typing, deleted his half-finished essay, left the library, the University and the country, and swore never to return.