In terms of spatial resolution, the analogue of DPI in offset printing is lines per inch (LPI). This describes how fine or coarse the halftone screen is. The greater the LPI, the more fine the details that can be represented in the printed image (and also, the higher the DPI that is required in the source file if you are starting from a digital image; rule of thumb is to multiply the print LPI by 1.5-2.0 to get the minimum source DPI).

LPI will affect the quality of photographic material, shaded regions, gradients, etc.

Here's a page I found in a quick search that explains this concept more fully and shows some examples: Understanding Halftones

I think that answers the question as you worded it. However, if you're generally interested about what will affect offset print quality....

The type of surface you're printing on will affect the fidelity of the halftone dots as well as how high an LPI you can practically achieve. For example, ink dots spread out in newsprint (leading to "dot gain"), whereas this is less of an issue on coated stock.

The brightness of the paper will affect how vivid the bright regions of your design can be.

Using spot colors can allow you to have a specific color appear perfectly solid instead of halftoned if it's not one of the CMYK inks.

All of these factors will affect the fidelity/accuracy of printed product, which as others have noted is what clients care about in the end. (Such as color matching, as vector said, and contrast as horatio said)

I suggest you talk with whoever will actually be doing your offset printing to find out what quality options they can offer in terms of the printing process, the material you're printing on, etc.

In terms of spatial resolution, the analogue of DPI in offset printing is lines per inch (LPI). This describes how fine or coarse the halftone screen is. The greater the LPI, the more fine the details that can be represented in the printed image (and also, the higher the DPI that is required in the source file if you are starting from a digital image; rule of thumb is to multiply the print LPI by 1.5-2.0 to get the minimum source DPI).

LPI will affect the quality of photographic material, shaded regions, gradients, etc.

Here's a page I found in a quick search that explains this concept more fully and shows some examples: Understanding Halftones

I think that answers the question as you worded it. However, if you're generally interested about what will affect offset print quality....

The type of surface you're printing on will affect the fidelity of the halftone dots as well as how high an LPI you can practically achieve. For example, ink dots spread out in newsprint (leading to "dot gain"), whereas this is less of an issue on coated stock.

The brightness of the paper will affect how vivid the bright regions of your design can be.

Using spot colors can allow you to have a specific color appear perfectly solid instead of halftoned if it's not one of the CMYK inks.

All of these factors will affect the fidelity/accuracy of printed product, which as others have noted is what clients care about in the end. (Such as color matching, as vector said, and contrast as horatio said)

I suggest you talk with whoever will actually be doing your offset printing to find out what quality options they can offer in terms of the printing process, the material you're printing on, etc.

In terms of spatial resolution, the analogue of DPI in offset printing is lines per inch (LPI). This describes how fine or coarse the halftone screen is. The greater the LPI, the more fine the details that can be represented in the printed image (and also, the higher the DPI that is required in the source file if you are starting from a digital image; rule of thumb is to multiply the print LPI by 1.5-2.0 to get the minimum source DPI).

LPI will affect the quality of photographic material, shaded regions, gradients, etc.

Here's a page I found in a quick search that explains this concept more fully and shows some examples: Understanding Halftones

I think that answers the question as you worded it. However, if you're generally interested about what will affect offset print quality....

The type of surface you're printing on will affect the fidelity of the halftone dots as well as how high an LPI you can practically achieve. For example, ink dots spread out in newsprint (leading to "dot gain"), whereas this is less of an issue on coated stock.

The brightness of the paper will affect how vivid the bright regions of your design can be.

Using spot colors can allow you to have a specific color appear perfectly solid instead of halftoned if it's not one of the CMYK inks.

All of these factors will affect the fidelity/accuracy of printed product, which as others have noted is what clients care about in the end. (Such as color matching, as vector said, and contrast as horatio said)

I suggest you talk with whoever will actually be doing your offset printing to find out what quality options they can offer in terms of the printing process, the quality of what you're printing on, etc.

In terms of spatial resolution, the analogue of DPI in offset printing is lines per inch (LPI). This describes how fine or coarse the halftone screen is. The greater the LPI, the more fine the details that can be represented in the printed image (and also, the higher the DPI that is required in the source file if you are starting from a digital image; rule of thumb is to multiply the print LPI by 1.5-2.0 to get the minimum source DPI).

LPI will affect the quality of photographic material, shaded regions, gradients, etc.

Here's a page I found in a quick search that explains this concept more fully and shows some examples: Understanding Halftones

I think that answers the question as you worded it. However, if you're generally interested about what will affect offset print quality....

The type of surface you're printing on will affect the fidelity of the halftone dots as well as how high an LPI you can practically achieve. For example, ink dots spread out in newsprint (leading to "dot gain"), whereas this is less of an issue on coated stock.

The brightness of the paper will affect how vivid the bright regions of your design can be.

Using spot colors can allow you to have a specific color appear perfectly solid instead of halftoned if it's not one of the CMYK inks.

All of these factors will affect the fidelity/accuracy of printed product, which as others have noted is what clients care about in the end. (Such as color matching, as vector said, and contrast as horatio said)

I suggest you talk with whoever will actually be doing your offset printing to find out what quality options they can offer in terms of the printing process, the material you're printing on, etc.