A few general aspects are discussed in [entry validation].

The validation is performed at two levels:

1. Weak validation:
   - Allow empty string or sign only
   - Verify sign
2. Strong validation:
   - Strong integer and range check
   - Change the entry background color to yellow/red on error

The "focusout" validation is optional, it can be removed.
Sample code:

    proc validInteger {win event X oldX min max} {
        # Make sure min<=max
        if {$min > $max} {
            set tmp $min; set min $max; set max $tmp
        }
        # Allow valid integers, empty strings, sign without number
        # Reject Octal numbers, but allow a single "0"
        # Which signes are allowed ?
        if {($min <= 0) && ($max >= 0)} {   ;# positive & negative sign
            set pattern {^[+-]?(()|0|([1-9][0-9]*))$}
        } elseif {$max < 0} {               ;# negative sign
            set pattern {^[-]?(()|0|([1-9][0-9]*))$}
        } else {                            ;# positive sign
            set pattern {^[+]?(()|0|([1-9][0-9]*))$}
        }
        # Weak integer checking: allow empty string, empty sign, reject octals
        set weakCheck [regexp $pattern $X]
        # if weak check fails, continue with old value
        if {! $weakCheck} {set X $oldX}
        # Strong integer checking with range 
        set strongCheck [expr {[string is int -strict $X] && ($X >= $min) && ($X <= $max)}]

        switch $event {
            key {
                $win configure -bg [expr {$strongCheck ? "white" : "yellow"}]
                return $weakCheck
            }
            focusout {
                if {! $strongCheck} {$win configure -bg red}
                return $strongCheck
            }
            default {
                return 1
            }
        }
    }

    proc checkForm {args} {
        set err 0
        foreach win $args {
            switch -- [$win cget -bg] {
                red -
                yellow {
                    incr err
                }
            }
        }
        if {$err} {
            tk_messageBox -type ok -icon error -message "Check $err invalid field(s)"
        } else {
            tk_messageBox -type ok -message "Changes applied successfully"
        }
    }

    set x1 12; set x2 345; set x3 -678

    label .t1 -text "int (10..92)"
    entry .e1  -textvariable x1 -validate all -vcmd {validInteger %W %V %P %s +10 +92} 
    label .t2 -text "int (-256..+1024)" 
    entry .e2 -textvariable x2 -validate all -vcmd {validInteger %W %V %P %s +1024 -256}
    label .t3 -text "int (-768..0)"
    entry .e3 -textvariable x3 -validate all -vcmd {validInteger %W %V %P %s -768 0}

    button .apply -text "Apply changes" -command {checkForm .e1 .e2 .e3}

    grid .t1 .e1 -sticky w
    grid .t2 .e2 -sticky w
    grid .t3 .e3 -sticky w
    grid .apply - -sticky ew

    catch {console show}

----
[Rolf Schroedter] using hints given by [Jeffrey Hobbs] and [DKF]