Hi,

In order to update multiple fields, you batch class would need some modifications -

Use a map of field names and values, instead of two variables field and value

global class BatchUpdateField implements Database.Batchable<sObject>{
global final String Query;
global final Map<String, String> fieldValues;
global BatchUpdateField(String q, Map<String, String> fieldValues){
Query = q;
this.fieldValues = fieldValues
}
global Database.QueryLocator start(Database.BatchableContext BC){
return Database.getQueryLocator(query);
}
global void execute(Database.BatchableContext BC, List<sObject> scope){  
for(sobject s : scope){
for(String fldName : fieldValues.keySet()) {

s.put(fldName, fieldValues.get(fldName));

}
}

update scope;
}
global void finish(Database.BatchableContext BC){  
AsyncApexJob a = [Select Id, Status, NumberOfErrors, JobItemsProcessed,TotalJobItems,CreatedBy.Email
from AsyncApexJob where Id = :BC.getJobId()];
string message = 'The batch Apex job processed ' + a.TotalJobItems + ' batches with '+ a.NumberOfErrors + ' failures.';
// Send an email to the Apex job's submitter notifying of job completion.
Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
String[] toAddresses = new String[] {a.CreatedBy.Email};
mail.setToAddresses(toAddresses);
mail.setSubject('Salesforce BatchUpdateField ' + a.Status);
mail.setPlainTextBody('The batch Apex job processed ' + a.TotalJobItems + ' batches with '+ a.NumberOfErrors + ' failures.');
Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });  
}

using the query for execution from systemlog:

Database.executebatch(batch,200);



In this example I have used a String map, considering all String values to be udpated. Modify the map to use an 'object' type , for varying type of field updates.

Hope this helps.