For improving marketing I was mainly thinking thought leadership like reports and guides around topics impacting potential/existing clients' businesses
For ensuring the best service I though the main thing would be having a real knowledge about the clients industry/business issues and also being proactive in terms of interacting with clients outside of the work the firm does for them
I agree with @Jessica Booker and think outside the box thinking can really show your tenacity and ability to think commercially. I would also add that with the first question, it might not just mean marketing the firm to clients. Remember to think beyond what you might first see/think, it could well relate to marketing the firm to potential hires, both prospective trainees and qualified lawyers currently at different firms! this can add a whole other dimension to your response and show your breadth of thought