The short answer (with respects to problems) is everything that comes along with capital. The good news is that there is significantly less red tape to cut through for innovation!
In my journey from working at a Fortune 100 firm to starting my own company, I had a "transition" working with a medium sized company.
As I moved from the large firm to the medium company, I noticed the number of resources drop off significantly and really gained an appreciation for how much information is free when you know how to look for it. In this setting, I found that I was actually able to be more innovative as I still had access to capital for innovation experiments and there were fewer barriers as far as corporate policies.
Moving from the medium company to my own startup, the resources obviously dropped off even further, this time with respect to capital. Of course, there is no problem as far as making the go/no-go decision on pursuing an innovative effort, but I also have to be clever with what type of front end studies are performed.
Innovation as a startup is essential and it's great fun when you figure out how cheaply evaluate efforts to determine if making a larger investment is viable. Feel free to reach out to me to discuss further!
Jeremy is absolutely right about resources in a firm. Capital is a huge issue.
One of the biggest issues a startup will face is the Built It/Buy It question. You need a new piece of technology or software to do business. Maybe you need a CRM, or a time tracking app for employees, or a document filing and stamping system. Should you buy a product already on the market or make your own? There's a lot of factors here that come into play such as speed to market and cost of development vs licensure.
Another issue that startups can run into is a lack of bandwidth. When you engage contract developers for work, make sure you discuss timelines and what their workload looks like. Is your team going to be dedicated to your project or are they working on other efforts. Hiring 1 developer to build something might seem like a great idea, but if they are working on 10 other projects, you might never get your product.
I hope this helps! If you have any other questions, please feel free to reach out!