There are very few disadvantages to liquidity per se, but in practice (and in a competitive financial market) there are downsides that more liquid assets (such as money) have over less liquid assets (such as factories).
The most important one is return, or lack thereof; more liquid assets usually don't pay very much interest, and are usually not the sort of thing that directly earns revenue by itself. If you keep your wealth in cash instead of investing it, you bear the opportunity cost of the return you could have made on those investments.
There are also often differences in how different assets are taxed; often more liquid assets are taxed higher than less liquid assets in an effort to incentivize investment.
In businesses specifically, excess liquidity is generally a sign that the company is being too risk-averse, and failing to invest in new ventures such as research that carry risk but can also yield great rewards. Cash is a safe asset (not perfectly safe, since there is inflation and currency exchange to worry about, but safer than most other assets), but in part because of this it actually yields a negative real return (due to inflation). Businesses often liquidate their assets and hold cash during recessions, because they fear the future; but this actually tends to exacerbate recessions by taking productive assets out of use and pulling cash out of circulation.
Wise business managers maintain a balance, keeping some liquidity in case they need it but not so much that they sacrifice the opportunity for investment returns.