Some relevant resources:

1. Chapter 3, "Exploring Unresolved Questions", in the Good Food Insitute's Student Guide.
2. The Science Behind Cultivated Meat, a series by Elliot Swartz. 
3. A very recent Nature review on the bottlenecks and current challenges in cultivated meat - Scientific, sustainability and regulatory challenges of cultured meat. It's paywalled, so let me know if you (or anyone else) needs help with that.

In addition to the answer by avacyn, which I endorse,  I'd like to add that there would probably be several generations of products. At first, it would likely be a mix of plants and a bunch of muscle/fat/stem cells. Later generations might include more sophisticated tissues and cell differentiation process which would be necessary for more complex meat such as steaks. As avacyn said, the industry is mostly focused on the short term and making first-generation products. Next-generation cultivated meat products would be in much better shape if we had more understanding of tissue engineering and developmental biology, and probably many other fields. 

In the abstract, the highest impact scientific research you can do outside industry should focus on things that are important to long-term success, but are not necessary in the short term. 

Companies already have a strong incentive to find alternatives to the largest cost-drivers so that they can begin to produce regularly at smaller scales without going bankrupt. For example, companies are likely already working on alternatives to using the most expensive growth factors, since at current costs, they can make even small scale production cost-prohibitive.

However, the long term success of cultivated meat will require innovation and cost reduction across the entire value chain. Many of these innovations aren't important for the short-term goals of the industry, so will likely get pushed off until later. This is where academic research can currently provide value.

One great candidate for this is developing ways to create dirt-cheap basal media from plants, e.g. using hydrolysates. Currently, basal media components are all sourced separately, and are often produced in inefficient ways. For example, individual amino acids are often produced via fermentation and then combined in a single media formulation. This is a much less efficient process compared to current meat production, where amino acids are sourced from soybeans and fed to animals. In the long term, it's likely that cultivated meat will need to move to a system where the main basal media components are grown via agriculture as opposed to biotech. However, it's likely difficult for companies to justify spending a lot of time on this, since basal media is not currently a major cost driver.

In addition to what avacyn said about hydrolysates (very important! Amino acids are really expensive!), off the top of my head:

• Figuring out ways to do extreme sanitation/fully aseptic operations cheaply at scale
  • mammal stem cells double every 21-48 hours, E.coli doubles every 25 minutes, if you have a giant bioreactor full of yummy meat cells + growth media at ph~=7.0 and temp~=37C, one stray bacterium or virus can ruin your day. 
  • maybe more of an engineering problem than a foundational science problem, but solving this would also be fairly helpful for a number of medical and other bioengineering scaleup questions
• novel(?) materials science that lets you build high-quality reusable bioreactors without being as expensive as stainless steel or "use and discard" as has become common(?) in biologics
• genetic engineering to create cells that have much longer lifespans (or are immortal), breaking the Hayflick limit.
• Other cell line genetic engineering, including but not limited to:
  • faster growth rates
  • higher metabolic efficiency
  • countering catabolite and CO2 inhibition
    • I'm not sure what catabolite inhibition actually does, biologically, but it sure seems important.
• Tissue engineering/scaffolding, useful both for adding structure to clean meat (eg in steaks) and (in the limit) for creating replacement body parts in surgery for humans
  • though I've been advised that scaffolding is unlikely to be the most significant bottleneck for cultured meat.