My view is that company formation and growth is hard enough - one has to deal with market risk, technology risk, team risk, downstream financing risk, etc; therefore deals that layer "bad organizational/legal hygiene" as an additional risk factor into the investment evaluation tend to fail to secure investment.
Cap table hygiene refers to practice of keeping a cap table up to date, accurate, easy to use, and clean of the type of issues that would cause key stakeholders (e.g. investors, board of directors, potential partners, acquirers, executives, or lawyers) to question the future of the company.
I group typical markers of cap table hygiene into two broad groups of issues, technical and practical.
While the math behind cap tables is fairly simple in most cases - addition, division, simple algebra - the terminology can be opaque, difficult to understand from legal documents, and easily misapplied, leading to unclear structures and incorrect calculations. Here's a few technical things I commonly check in cap tables:
- Share price calculations. Easy to make errors with conversions and new option pools.
- SAFE and Convertible Note conversions. Easy to make errors on conversion methods, calculating share price, rounding of shares (or mistaken fractional shares), or calculating the share price using common conventions for the type of investment without reviewing the terms of the actual agreement.
- Cap tables that exclude share counts. I see this sometimes where a cap table cites ownership percentages but does not show share counts. That invites questions over the math, which is usually wrong.
Practical considersations bundles potential narrative, business strategy, and executional issues that may be hidden in the capital structure, ownership incentives, or past decisions made by the company. Here's a few I look for:
- First and foremost, cap tables should be up-to-date and regularly maintained. Cap tables that aren't updated invite questions about business infrastructual management and record-keeping, and create lots of catchup work when it is necessary to work through changes in capital structure that impact shareholders.
- Too many founders. As Will Price points out, too many founders means too small ownership to sustain dilution over multiple rounds, potentially reducing founder ownership below what is required to keep the founders incented to maximize the value of the equity of the company. It also points to potential issues later down the line with founder dynamics, splintered decision-making, and unclear executional strategy with a lot of founders (greater than 2 or 3) guiding the company. Who's in charge?
- Too many shareholders. The issue with too many shareholders is that, not properly handled, it can create practical and logistical issues with executing decisions requiring shareholder consents. It is common to raise money from many institutional and angel investors (and beneficial if they are strategically leveraged), but too many can create fundraising narrative issues (e.g. why did the company need to get this many investors? were they unable to get committed investors to write larger checks? can they leverage their investors) and logistical issues with shareholder agreements. 
- Dead equity. The issue with "dead equity" is equity that is owned by former executives, advisors, and partners no longer actively involved in growing the business. Too much equity owned by people no longer involved in the day to day operations or active in growing the value of the equity can create create a damper on the people still involved in the business, as other are benefiting without doing the work.
- Founders with not enough equity. The issue with founders not owning enough equity is that it may damper the incentives of founders and key executives to grow the equity value of the business. What's "too little" varies by stage; at early stages they need to have enough to last through the dilution from expected later rounds. "Too little" also varies over time and by region; current expectations of ownership by founders and key executives are generally higher than they were 20 years ago, and expectations can also vary widely by geography and local venture funding markets.
- Nonstandard terms for preferred investors. Do the participation rights of preferred investors make sense for the stages raised? Are there dividends or preferred returns baked into their agreements? Are other terms standard for the stages raised?
- Liquidity preferences. Does the amount of capital raised to date, and the liquidity preferences on that capital, make sense given the current state of the business, future growth, and capital needs? Has the company used its capital efficiently? Does the current valuation make sense compared to the amount of capital raised?
- Nonstandard vesting schedules, or no vesting schedules at all. The key question is whether founders have vesting schedules, and are incented to stay and grow the equity valuation of the company. Nonstandard vesting schedules could point to inexperienced founders that did not know better, or experienced founders getting too much value for their contributions.
Maintaining cap table hygiene is critical
It is important for you, someone at your company, or a trusted advisor (e.g. attorney) knows how to manage and maintain the cap table, and makes changes when needed.
The cap table may be in a spreadsheet or a web service (e.g. Carta, Pulley, Shareworks, LTSE, or others); spreadsheets work for analysis and scenario planning, but web services have a number of advantages in terms of managing records, staying abreast of rules, handling complicated calculations, managing vesting schedules and option plans, and more. Regardless of what tool you use, it is important that you/team/advisor keeps the cap table up-to-date and accurate at all times.