Details!

Examples of a non-diversified  fund:
Marsico Focus
Oakmark Select

"Closet index fund"
Actively managed fund that has performance close to that of an index fund but with much higher expenses

"After-tax returns" are important if you plan to add a fund to your non-retirement accounts.

Low-minimum funds: $50 minimum to open an account at  Artisan funds or T. Rowe Price if you sign up for  automatic monthly investments. 

Fund Details

Fund Prospectus/Annual Report

Read the prospectus carefully before you invest.
"The Fund in Detail" gives overall goal of the fund e.g. Income
"Investment Principles and Risk" section tells what the fund invests in
and the risks.
"Financial Highlights" section offers performance information (return,
return relative to a index, etc.)
"Fees and Expenses" section shows Expense ratio, Loads, etc.
"Your account" section has the phone numbers, types of accounts etc.

The annual report lists in detail all the securities in the fund's portfolio including sector/country allocations. Fund performance and sometimes a commentary on the fund performance/markets is also included. A Statement of additional information (SAI) supplements what is already disclosed in the prospectus.

Fund/Fund Family/Fund Supermarket

All funds belong to a Fund family that usually has multiple funds to offer. An investor can buy funds from different fund families through a fund supermarket such as Schwab, Fidelity or Scottrade. Advantages are a consolidated statement and ability to sell a fund from one fund family and move it into another, a great feature for IRA’s where transfers can take quite long. Research carefully details such as minimums, fees on some funds outside the network, redemption fees etc.
 
Minimum investment (and other services):
May depend on kind of account (regular, IRA, custodial). Some fund families waive the minimum investment if automatic investment plan is chosen. (e.g. T. Rowe Price or Artisan). Other low minimum funds can be found at MFEA.

Your Portfolio Design: Choice of a fund also depends on how it complements other funds in your portfolio.

Time period for return: Always compare two funds over the same time period.

Consistency of return: Some funds consistently have good returns, others have very good returns one year and a poor performance the next year.

Performance relative to index: Compare a fund's return to an appropriate index. Use the graphing tool at Yahoo (here we compare Fidelity Contrafund vs. the SP500 index)

Performance relative to Peers: Compare a fund's return also to its peers. Use the graphing tool at Yahoo (here we compare Fidelity Contrafund vs. Fidelity Capital Appreciation).

Performance relative to assumed risk: Use metrics such as alpha and sharpe ratio to determine performance of a manager relative to the risk that the manager takes.

Before/After tax returns: Some funds are tax efficient (they do not pay out large or any distributions) while some are very tax inefficient. Tax efficient funds may be a wise choice in a regular (non-retirement) account.

Style/Performance of Manager: Check how closely the manager follows the stated style. Follow the performance of the manager, it is often as important as following the performance of the fund. A new fund with a star manager may be expected to do well.

Tenure of the Fund Manager: How long the manager has been at the helm of the fund. A new manager may not be necessarily bad especially if his/her previous experience was running a highly rated fund. 

Manager changes: A fund may have a terrific performance record under the helm of a manager who has recently quit managing that fund.  

Manager stake: How much of the fund managers own money is invested in the fund.

Fund Fiduciary Grade: Available at Morningstar

Individual manager/Team managers: Some funds are team managed, most funds are individually managed.

Diversified/Non-diversified funds: Some funds are diversified (e.g. 150 stocks in the portfolio) while some are non-diversified (e.g. 30 stocks). Non-diversified funds are generally more risky.  

Fund Assets/Asset Growth: Assets of a fund are important especially for small cap funds. Large assets make it difficult in taking large positions in promising small companies. Growth of assets indicate how much and how fast the money is coming into the fund. If this is too high, underperformance may result if the fund manager cannot deploy these funds effectively. Some managers address this issue by closing the funds to new money (soft close: fund accepts new money from only existing investors but not new investors, hard close: fund does not accept any new money).